/J- 


SPREADING  CONCRETE  OVER  REINFORCING  STEEL  BY 

MEANS  OF  TOWER  AND  DISTRIBUTING  CHUTE 

Courtesy   of  Leonard   Construction    Company,    General   Con- 

tractoryf   Chicayo 


CONCRETE  AND  REINFORCED 
CONCRETE  ^ 


A    CONDENSED     PEACTICAL    TREATISE    ON    THE 
PROBLEMS    OF    CONCRETE    CONSTRUCTION, 
INCLUDING  CEMENT  MIXTURES,  TESTS, 
BEAM    AND    SLAB    DESIGN,   CON- 
(       STRUCTION  WORK,  RETAIN- 
ING   WALLS,     ETC. 


BY 

WALTER  LORING  WEBB,  C.  E. 

CONSULTING  CIVIL  ENGINEKK 
AUTHOR  OF  "RAILROAD  CONSTRUCTION",  "ECONOMICS  OF 

RAILROAD   CONSTRUCTION",   ETC. 
AMERICAN  SOCIETY  OF  CIVIL  ENGINEERS 

AND 

W.  HERBERT  GIBSON,  B.  S.,  C.  E. 

CONSULTING     ENGI  NT.r.R 

SPECIALIST    IN    REINFORCED    CONCRETE 
AMERICAN    SOCIETY'    OF    CIVIL    ENGINEERS 


ILLUSTRATED 


AMERICAN  TECHNICAL  SOCIETY 
CHICAGO 
1919 


COPYRIGHT,    1916,    BY 

AMERICAN  TECHNICAL  SOCIETY 


COPYRIGHTED     IN    GREAT    BRITAIN 
ALL  RIGHTS   RESERVED 


INTRODUCTION 

/^ONCRETE  has  in  a  comparatively  short  span  of  years  be- 
^•^  come  one  of  the  most  useful,  if  not  the  most  useful,  sub- 
stance in  the  hands  of  the  constructor.  Its  many  forms 
include  the  simpler  monolithic  construction  as  a  substitute 
for  stone  as  well  as  the  more  complicated  reinforced  con- 
crete types.  The  interest  of  the  reading  public  in  this 
subject  makes  an  authoritative  yet  condensed  treatise  par- 
ticularly timely. 

t  In  the  preparation  of  this  volume  the  author  has  en- 
deavored to  present  the  subject  in  a  simple  and  concise 
manner  suitable  for  both  engineers  and  students.  The  com- 
position and  treatment  of  cement,  sand,  stone,  and  mortar, 
the  mixtures  commonly  used,  the  steel  for  reinforcing,  and 
the  nreproofing  qualities  of  concrete  are  all  sufficiently  dis- 
cussed to  give  accurate  knowledge  of  their  relation  to  the 
general  subject  in  hand.  The  general  theory  of  flexure  in 
reinforced  concrete,  the  author  has  taken  particular  pains 
to  make  clear  and  simple.  This  is  also  true  of  the  design 
of  the  ordinary  beam  and  girder  type  of  floor,  special  refer- 
ence being  made  to  the  bonding  of  steel  and  concrete, 
vertical  shear,  and  diagonal  tension.  The  text  includes 
tables  and  diagrams  by  means  of  which  designs  may  be 
made  without  the  use  of  other  portions  of  the  text. 

826533 


REINFORCED  CONCRETE 

If  Other  important  features  are  the  treatment  of  flat-slab 
construction,  which  is  complete  and  in  accordance  with  the 
best  engineering  practice;  the  design  of  simple  and  com- 
pound footings;  gravity  and  reinforced  retaining  walls;  cul- 
verts; girders;  and  miscellaneous  structures.  The  remainder 
of  the  book  is  devoted  to  construction  work,  covering  equip- 
ment, methods  of  mixing  and  transporting  concrete,  form 
work  for  columns,  slabs,  beams,  and  walls,  and  the  proper 
location  of  construction  joints.  To  drive  these  suggestions 
home  a  number  of  typical  examples  of  reinforced  concrete 
construction,  such  as  buildings,  bridges,  large  sewers,  and 
tanks,  are  fully  analyzed. 

f  Altogether,  the  treatise  gives  just  the  material  the  engi- 
neer or  contractor  needs  for  his  work,  or  that  the  layman 
will  find  interesting  for  his  general  reading.  It  is  the  hope 
of  the  publishers  that  the  book  will  prove  of  distinct  value 
in  the  field  of  concrete  construction. 


CHICAGO   SERVICE   BUILDING   OF   FORD   MOTOR   COM- 
PANY, SHOWING  MODERN  CONCRETE  CONSTRUCTION 
Courtesy    of    the    Condron    Company,    Chicago 


CONTENTS 

PAGE 

Composition  and  treatment. 1 

Cement   1 

Sand    6 

Broken  stone 10 

Mortars 12 

Characteristics  and  properties  of  concrete  mixtures 14 

Mixing  and  laying  concrete 21 

Methods  of  proportioning 21 

Wetness  of  concrete 25 

Methods  of  mixing 27 

Problems  in  laying 29 

Waterproofing  concrete 35 

Preservation  of  steel  in  concrete 41 

Fire  protective  qualities  of  concrete 43 

Steel  for  reinforcing  concrete 45 

General  theory  of  flexure  in  reinforced  concrete 50 

Statics  of  plain  homogeneous  beams * 51 

Statics  of  reinforced  concrete  beams 53 

Elasticity  of  concrete  in  compression 54 

Theoretical  assumptions 54 

Summation  of  compressive  forces 55 

Center  of  gravity  of  compressive  forces 56 

Position  of  neutral  axis 56 

Values  of  moduli  of  elasticity 57 

Percentage  of  steel 60 

Resisting  moment 61 

Practical  calculation  and  design  of  beams  and  slabs 67 

Tables  for  slab  computations 67 

Table  for  computation  of  simple  beams 72 


CONTENTS 

Practical  calculation  and  design  (Continued)  PAGQ 

Bonding  steel  and  concrete 74 

Vertical  shear  and  diagonal  tension 78 

Methods  of  guarding  against  failure  by  shear  or  by 

diagonal  tension 79 

Calculations  by  diagrams  of  related  factors 80 

Slabs  on  I-beams 83 

Slabs  reinforced  in  both  directions 84 

Reinforcement  against  temperature  cracks 85 

T-Beam  construction , 86 

Resisting  moments  in  T-beams.. 87 

Width  of  flange 90 

Width  of  rib 91 

Shearing  stresses  between  beam  and  slab 93 

Shear  in  a  T-beam 96 

Illustration  of  slab,  beam,  and  girder  construction. . .  97 

Simple  footings   104 

Wall  footing 104 

Column  footing 106 

Continuous  beams    Ill 

Compound  footings   Ill 

Conditions  demanding  compound  footings Ill 

Practical  treatment  of  problem 112 

Piles    116 

Capping  and   driving 117 

Design 118 

Loading    119 

detaining  walls 123 

Failures  of  walls 124 

Foundations  for  wall 125 

Fill  behind  wall 126 

Design  of  wall 126 

Reinforced  concrete  walls , 132 

Reinforced  concrete  walls  with  counterforts 139 


CONTENTS 

PAGE 

Culverts    145 

Girder  bridges 150 

Concrete  building  blocks 154 

Fence  posts  158 

Silos 100 

Concrete  walks 161 

Concrete  curb   166 

Concrete  construction  v,  or j: 170 

Machinery  for  concrete  work 170 

Concrete  mixers   170 

Hoisting  and  transporting1  equipment 173 

Machinery  for  miscellaneous  operations 177 

Forms 180 

Building  forms 180 

Forms  for  sewers  and  walls 185 

Forms  for  centers  of  arches 187 

Finishing  surfaces  of  concrete 193 

Bending  or  trussing  bars 201 

Bonding  old  and  new  concrete 206 

Details  of  construction , 208 

Typical  examples  of  reinforced  concrete  construction  210 

Flat-slab  construction 219 

Placing  reinforcing  bars 

Method  of   calculation 

Location  of  bars 

General  constructive  details 

Index .  229 


CONCRETE  AND  REINFORCED 
CONCRETE 

Concrete  as  a  substitute  for  masonry  has,  in  a  compara- 
tively few  years,  earned  a  very  important  place  for  itself  in 
engineering  and  building  work.  In  the  early  years  of  its  use, 
before  a  proper  judgment  as  to  its  limitations  had  been  formed, 
failure  of  concrete  structures  created  a  prejudice  against  the 
material,  but  this  has  now  been  dispelled.  The  evolution  of  the 
product  has  served  to  standardize  concrete  as  a  material,  and 
exhaustive  experiments  and  theoretical  deductions  supplied  by 
eminent  engineers  have  so  standardized  the  designs  of  rein- 
forced concrete  structures  that  failures  have  become  practi- 
cally unknown.  The  cheapness  of  concrete  and  its  adaptability 
to  all  forms  of  construction,  particularly  those  of  monolithic 
character,  have  resulted  in  wider  and  wider  applications  of  the 
material. 

Concrete  is  composed  of  a  mixture  of  cement,  sand,  and 
crushed  stone  or  gravel,  which,  after  being  mixed  with  water, 
soon  sets  and  obtains  a  hardness  and  strength  equal  to  that 
of  a  good  building  stone.  A  study  of  the  materials  compos- 
ing concrete  and  of  the  effect  of  varying  the  proportions  of 
these  materials  will  be  helpful  before  taking  up  the  questions 
of  design  and  erection  of  concrete  structures. 

COMPOSITION  AND  TREATMENT 
CEMENT 

Cement  is  manufactured  by  properly  burning,  cooling,  and 
grinding  a  composition  of  argillaceous  and  calcareous  materials. 
The  burning  and  cooling  require  great  care,  for  complicated 
chemical  reactions  take  place  during  the  process.  After  cool- 
ing, the  mass  is  ground  into  a  powder,  most  of  which  will  pass 
a  wire  sieve  having  200  wires  per  lineal  inch.  Very  fine  cements 
are  better  than  the  coarser  varieties,  other  things  being  equal. 


2  .-REINFORCED  CONCRETE 

la  «01or,  c^m^nt  varies  through  the  different  shades  of  grays, 
depending  on  the- calor  of  the  stone  from  which  it  is  made. 

Cement,  when  mixed  with  water  and  allowed  to  set,  will 
harden  in  a  few  hours,  and  should  develop  a  greater  part  of 
its  ultimate  strength  in  a  few  days.  It  is  permanent  in  the 
respect  that  no  essential  change  in  form  or  volume  will  take 
place,  either  on  account  of  inherent  qualities,  or  as  the  result 
of  exterior  agencies.  There  is  always  a  slight  shrinkage  in 
the  volume  of  cement  or  concrete  during  the  process  of  setting 
and  hardening,  but  with  good  cement  this  shrinkage  is  not  so 
great  as  to  be  objectionable. 

Classification  of  Cement.  Portland  cement  and  natural 
cement  are  the  two  principal  cements  in  common  use. 

Natural  Cement.  Natural  cement  is  obtained  by  burning 
argillaceous  limestone,  which,  in  its  natural  state,  has  the  proper 
chemical  composition.  Such  cement  was  formerly,  and  is  some- 
times still,  called  Rosendale  cement,  from  the  fact  that  it  was 
first  produced  in  Rosendale,  New  York.  Rock  from  which 
natural  cement  can  be  made  is  found  in  diffevent  sections  of 
the  country. 

Natural  cement  is  not  so  uniform  in  composition  as  Portland 
cement,  and,  therefore,  not  so  reliable.  It  is  quick  setting  and 
requires  more  water  in  mixing  than  Portland  cement.  Since 
the  cement  is  made  wholly  from  the  rock  just  as  the  latter  is 
taken  out  of  the  quarry,  and  since  the  rock  is  calcined  at  a 
much  lower  temperature  than  that  employed  in  making  Port- 
land cement,  natural  cement  is  considerably  cheaper  than 
Portland  cement.  It  weighs  300  pounds  per  barrel  of  about  4 
cubic  feet.  Natural  cement  is  employed  only  on  account  of 
its  cheapness,  and  only  when  low  stresses  are  used  or  quick  set- 
ting is  required.  It  should  never  be  used  for  reinforced  con- 
crete work. 

Portland  Cement.  Portland  cement  is  obtained  from  the  cal- 
cination to  incipient  fusion  of  a  thorough  mixture  of  propor- 
tioned argillaceous  and  calcareous  materials.  It  is  made  in 
many  sections  of  the  country  and  is  now  in  common  use ;  unless 
natural  cement  is  especially  mentioned,  Portland  cement  is  the 


REINFORCED  CONCRETE  3 

grade  which  is  referred  to.  It  is  much  stronger  than  natural 
cement  and  more  nearly  uniform  in  all  of  its  properties.  A 
barrel  of  Portland  cement  usually  contains  3.0  cubic  feet  and 
weighs  384  pounds  net.  The  cement  is  generally  put  up  in 
bags,  each  containing  TO  cubic  foot  and  weighing  90  pounds, 
that  is,  one-fourth  of  a  barrel. 

Portland  cement  is  extensively  used.  It  is  essential  in  rein- 
forced concrete  work  and  when  concrete  is  laid  under  water  or 
is  subjected  to  severe  and  repeated  stresses.  A  preliminary 
report  which  was  made  by  the  U.  S.  government  shows  that  ap- 
proximately 88,514,000  barrels  of  cement  were  made  in  the 
United  States  during  1914;  the  production  for  1913  was  92,- 
097,131  barrels.  These  figures  indicate  the  great  importance 
of  cement  today  in  all  sorts  of  construction  work. 
Standard  Cement  Specifications 

A  committee  of  the  American  Society  for  Testing  Materials 
presented  to  that  body  the  following  report  on  cement  testing:* 

GENERAL,  OBSERVATIONS 

1.  These  remarks   have  been  prepared  with  a  view  to  pointing  out 
the   pertinent   features   of   the    various   requirements   and    the   precau- 
tions to  be  observed  in  the  interpretation  of  the  results  of  the  tests. 

2.  The    committee   would    suggest   that   the   acceptance   or   rejection 
under  these  specifications  be  based  on  tests  made  by  an  experienced 
person  having  the  proper  means   for  making  the  tests. 

Specific  Gravity 

3.  Specific    gravity    is    useful    in    determining    adulteration.       The 
results   of  tests   of  specific  gravity  are   not   necessarily    conclusive   as 
an  indication   of  the  quality   of  a   cement,   but  when   in    combination 
with  the  results  of  other  tests  may  afford  valuable  indications. 

Fineness 

4.  The  sieves  should  be  kept  thoroughly  dry. 

Time  of  Setting 

5.  Great  care  should  be  exercised  to  maintain  the  test  pieces  under 
as  uniform  conditions  as  possible.     A  sudden  change  or  a  wide  range 
of  temperature  in  the  testing  room,  a  very  dry  or  humid  atmosphere, 
and  other  irregularities  vitally  affect  the  rate  of  setting. 

Constancy  of  Volume 

6.  The  tests  for  constancy  of  volume  are  divided  into  two  classes, 
the   first   normal,    the   second    accelerated.      The    latter   should    be   re- 


*Adopted  August  16,  1909,  except  the  sections  on  methods  of  testing 
cement  referred  to  in  §9  p.  4  which  were  adopted  January  17,  1912. 


4  REINFORCED  CONCRETE 

garded  as  a  precautionary  test  only,  and  not  infallible.  So  many 
conditions  enter  into  the  making  and  interpreting  of  it  that  it  should 
be  used  with  extreme  care. 

7.  In   making   the    pats,   the   greatest   care   should   be   exercised    to 
avoid  initial  strains  due  to  molding  or  to  too  rapid  drying-out  during 
the   first   24    hours.      The   pats    should    be    preserved   under   the   most 
uniform  conditions  possible,  and  rapid  changes  of  temperature  should 
be  avoided. 

8.  The   failure   to    meet    the    requirements   of   the   accelerated    tests 
need  not  be  sufficient  cause  for  rejection.     The  cement,  however,  may 
be  held   for  28   days,   and   a   retest   made   at   the  end  of  that  period, 
using  a  new  sample.     "Failure  to  meet  the  requirements  at  this  time 
should   be    considered    sufficient    cause   for   rejection,   although    in    the 
present  state   of  our  knowledge  it  cannot  be   said  that  such   failure 
necessarily  indicates   unsoundness,   nor   can  the  cement  be   considered 
entirely  satisfactory  simply   because  it  passes  the  tests. 

General  Conditions 

1.  All  cement  shall  be  inspected. 

2.  Cement  may  be  inspected  at  the  place  of  manufacture  or  on  the 
work. 

30  In  order  to  allow  ample  time  for  inspecting  and  testing,  the 
cement  should  be  stored  in  a  suitable  weather-tight  building  having 
the  floor  properly  blocked  or  raised  from  the  ground. 

4.  The  cement  shall  be  stored  in  such  a  manner  as  to  permit  easy 
access  for  proper  inspection  and  identification  of  each  shipment. 

5.  Every  facility  shall  be  provided  by  the  contractor,  and  a  period 
of  at  least  12  days  allowed  for  the  inspection  and  necessary  tests. 

6.  Cement   shall  be  delivered  in  suitable  packages,   with  the  brand 
and  name  of  manufacturer  plainly  marked  thereon. 

7.  A  bag  of  cement  shall  contain  94  pounds  of  cement  net.     Each 
barrel   of  Portland   cement  shall   contain   4   bags,   and   each   barrel   of 
natural  cement  shall  contain  3  bags  of  the  above  net  weight. 

8.  Cement    failing    to    meet    the    7-day    requirements    may    be    held 
awaiting  the  results  of  the  28-day  tests  before  rejection. 

9.  All  tests  shall  be  made  in  accordance  with  the  methods  proposed 
by  the  Special  Committee  on  Uniform  Tests  of  Cement  of  the  Amer- 
ican  Society  of  Civil  Engineers,  presented  to  the  Society  on  January 
17,   1912,   with   all   subsequent  amendments   thereto. 

10.  The   acceptance    or   rejection    shall   be    based   on    the   following 
requirements  : 

NATURAL  CEMENT 

11.  This  term  shall  be  applied  to  the  finely  pulverized  product  re- 
sulting  from   the   calcination    of   an   argillaceous   limestone  at  a   tem- 
perature only  sufficient  to  drive  off  the  carbonic  acid  gas. 

Fineness 

12.  It  shall  leave  by  weight  a  residue  of  not  more  than  10  per  cent 
on  the  No.  100,  and  30  per  cent  on  the  No.  200  sieve. 


REINFORCED  CONCRETE  5 

Time  of  Setting 

13.  It  shall  not  develop  initial  set  in  less  than  10  minutes,  and  shall 
not  develop  hard  set  in  less  than  30  minutes,  or  more  than  3  hours. 

Tensile  Strength 

14.  The   minimum   requirements   for   tensile   strength   for  briquettes 
1   square   inch   in    cross   section    shall    be   as    follows,   and    the   cement 
shall  show  no  retrogression  in  strength  within  the  periods  specified  : 

Neat  Cement 

AGE  STRENGTH 

24  hours    in    moist   air 75  Ib. 

7  days  (1  day  in  moist  air,  6  days  in  water) 150  " 

28  days  (1  day  in  moist  air,  27  days  in  water) 250  " 

One  Part  Cement,  Three  Parts  Standard  Ottawa  Sand 

7  days  (1  day  in  moist  air,  6  days  in  water) 50  Ib. 

28  days  (1  day  in  moist  air,  27  days  in  water) 125  " 

Constancy  of  Volume 

15.  Pats  of  neat  cement  about  3  inches  In  diameter,   \  inch  thick 
at  the  center,  tapering  to  a  thin  edge,  shall  be  kept  in  moist  air  for 
a  period  of  24  hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature. 

(b)  Another  is  kept  in  water  maintained  as  near  70°    F.   as  prac- 
ticable. 

1C.  These  pats  are  observed  at  intervals  for  at  least  28  days,  and, 
to  pass  the  tests  satisfactorily,  should  remain  firm  and  hard  and 
show  no  signs  of  distortion,  checking,  cracking,  or  disintegrating. 

PORTLAND  CEMENT 

17.  This  term  is  applied  to  the  finely  pulverized  product  resulting 
from   the   calcination    to   incipient   fusion   of   an   intimate    mixture   of 
properly  proportioned  argillaceous  and  calcareous  materials,  to  which 
no    addition    greater    than    3    per    cent  has  been   made   subsequent  to 
calcination.  -an        -, 

Specific  Gravity 

18.  The    specific    gravity    of    cement    shall    be    not    less    than    3.10. 
Should  the  test  of  cement  as  received  fall  below  this  requirement,  a 
second   test   may    be    made   on    a    sample   ignited   at  a    low   red   heat. 
The  loss  in  weight  of  the  ignited  cement  shall  not  exceed  4  per  cent. 

Fineness 

19.  It  shall  leave  by  weight  a  residue  of  not  more  than  8  per  cent 
on  the  No.  100,  and  not  more  than  25  per  cent  on  the  No.  200  sieve. 

Time  of  Setting 

20.  It   shall   not  develop  initial  set   in   less   than   30  minutes ;  and 
must  develop   hard   set  in   not   less   than    1   hour,  nor  more   than   10 
hours. 

Tensile  Strength 

21.  The  minimum   requirements   for  tensile   strength   for  briquettes 


6  REINFORCED  CONCRETE 

1    square   inch   in   cross   section   shall   be    as   follows,    and   the    cement 
shall   show   no  retrogression  in  strength  within   the   periods  specified  : 

Neat  Cement 

AGK  STRENGTH 

24  hours   in    moist   air .  175  Ib. 

7  days  (1  day  in  moist  air,  6  days  in  water) 500  " 

28  days  (1  day  in  moist  air,  27  days  in  water) 600  " 

One  Part  Cement,  Three  Parts  Standard  Ottawa  Sand 

1  days  (1  day  in  moist  air.  6  days  in  water) 200  Ib. 

28  days  (1  day  in  moist  air,  27  days  in  water) 275  " 

Constancy  of  Volume 

22.  Pats  of  neat  cement  about  3   inches  in  diameter,   J   inch  thick 
at  the  center,  and  tapering  to  a  thin  edge,  shall  be  kept  in  moist  air 
for  a  period  of  24  hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature  and  observed 
at  intervals  for  at  least  28  days. 

(&)  Another  pat  is  kept  in  water  maintained  as  near  70°  F.  as 
practicable,  and  observed  at  intervals  for  at  least  28  days. 

(c)  A  third  pat  is  exposed  in  any  convenient  way  in  an  atmos- 
phere of  steam,  above  boiling  water,  in  a  loosely  closed  vessel  for 
5  hours. 

23.  These  pats,  to  pass  the  requirements  satisfactorily,  shall  remain 
firm   and   hard,   and   show   no   signs  of  distortion,   checking,   cracking, 
or  disintegrating. 

Sulphuric  Acid  and  Magnesia 

24.  The  cement  shall  not  contain  more  than  1.75  per  cent  of  anhy 
drous   sulphuric   acid    (SO3),   nor   more   than   4   per   cent   of   magnesia 
(MgO). 

SAND 

Sand  is  a  constituent  part  of  mortar  and  concrete.  The 
strength  of  the  masonry  is  dependent  to  a  considerable  extent 
on  the  qualities  of  the  sand,  and  it  is  therefore  important  that 
its  desirable  and  defective  qualities  be  understood,  and  that 
these  qualities  be  always  investigated  as  thoroughly  as  are  the 
qualities  of  the  cement  used.  There  have  been  many  failures 
of  structures  due  to  the  use  of  poor  sand. 

Value.  Sand  is  required  in  mortar  or  concrete  for  the 
sake  of  economy,  and  to  prevent  the  excessive  cracking  that 
would  take  place  in  neat  lime  or  cement  without  it.  Mortar 
made  without  sand  would  be  expensive,  and  the  neat  lime  or 
cement  would  crack,  so  badly  that  the  increased  strength,  due 
to  the  neat  paste,  would  be  of  little,  if  any,  value. 


REINFORCED  CONCRETE  7 

Geological  Character.  Quartz  sand  is  the  most  durable  and 
•unchangeable.  Sands  that  consist  largely  of  grains  of  feldspar, 
mica,  hornblende,  etc.,  which  will  decompose  upon  prolonged 
exposure  to  the  atmosphere,  are  less  desirable  than  quartz, 
although  after  being  made  up  into  the  mortar,  they  are  vir- 
tually protected  against  further  decomposition. 

Essential  Qualities.  The  word  sand  as  used  above  is 
intended  as  a  generic  term,  to  apply  to  any  finely  divided  mate- 
rial which  will  not  injuriously  affect  the  cement  or  lime,  and 
which  is  not  subject  to  disintegration  or  decay.  Sand  is  almost 
the  only  material  which  is  sufficiently  cheap  and  which  will 
fulfil  these  requirements^  although  stone  screenings  (the  finest 
material  coming  from  a  stone  crusher),  powdered  slag,  and 
even  coal  dust  have  occasionally  been  used  as  substitutes. 
Specifications  usually  demand  that  the  sand  shall  be  "sharp, 
clean,  and  coarse/'  and  these  terms  have  been  repeated  so  often 
that  they  are  accepted  as  standard,  in  spite  of  the  frequent 
demonstrations  that  modifications  of  the  terms  are  not  only 
desirable  but  would  also  be  economical.  These  words  also 
ignore  other  qualities  which  should  be  considered,  especially 
when  deciding  between  two  or  more  different  sources  of  sand 
supply. 

Coarseness.  A  mixture  of  coarse  and  fine  grains,  with  the 
coarse  grains  predominating,  is  found  very  satisfactory,  as  it 
makes  a  denser  and  stronger  concrete  with  a  less  amount  of 
cement  than  when  coarse-grained  sand  is  used  alone  with  the 
same  proportion  of  cement.  The  small  grains  of  sand  fill  the 
voids  caused  by  the  coarse  grains  so  that  there  is  not  so  great 
a  volume  of  voids  to  be  filled  by  the  cement.  Very  fine  sand 
may  be  used  alone,  but  it  makes  a  weaker  concrete  than  either 
coarse  sand  or  coarse  and  fine  sand  mixeo!.  A  mortar  consisting 
of  very  fine  sand  and  cement  will  not  be  so  dense  as  one  of 
coarse  sand  and  the  same  cement,  although,  when  measured 
.or  weighed  dry,  both  contain  the  same  proportion  of  voids 
and  solid  matter.  In  a  unit  measure  of  fine  sand,  there  are 
more  grains  than  in  a  unit  measure  of  coarse  sand,  and,  'there- 
fore, more  points  of  contact.  More  water  is  required  in  gaging 


8  REINFORCED  CONCRETE 

a  mixture  of  fine  sand  and  cement  than  in  a  mixture  of  coarse 
sand  and  the  same  cement.  The  water  forms  a  film  and  sep- 
arates the  grains,  thus  producing  a  larger  volume  having  less 
density. 

The  screenings  of  broken  stone  are  sometimes  used  instead 
of  sand.  Tests  frequently  show  a  stronger  concrete  when 
screenings  are  used  than  when  sand  is  used.  This  is,  perhaps, 
due  to  the  variable  sizes  of  the  screenings,  which  would  have  a 
lower  percentage  of  voids. 

Sharpness.  The  sharpness  of  sand  can  be  determined  ap- 
proximately by  rubbing  a  few  grains  in  the  hand,  or  by  crush- 
ing it  near  the  ear  and  noting  if  a  grating  sound  is  produced ; 
but  an  examination  through  a  snfall  lens  is  a  better  method. 
Experiments  have  shown  that  round  grains  of  sand  have  fewer 
voids  than  do  angular  grains,  and  that  water-worn  sands  have 
from  3  per  cent  to  5  per  cent  fewer  voids  than  corresponding 
sharp  grains.  In  many  parts  of  the  country  where  it  is  impos- 
sible, except  at  a  great  expense,  to  obtain  the  sharp  sand,  the 
round  grain  is  used  with  very  good  results.  Laboratory  tests 
made  under  conditions  as  nearly  identical  as  possible  show 
that  the  round-grain  sand  gives  as  good  results  as  the  sharp 
sand.  In  consequence  of  such  tests,  the  requirement  that  sand 
shall  be  sharp  is  now  considered  useless  by  many  engineers, 
especially  when  it  leads  to  additional  cost. 

Cleanness.  In  all  specifications  for  concrete  work  is  found 
the  clause:  "The  sand  shall  be  clean."  This  requirement  is 
sometimes  questioned,  as  experimenters  have  found  that  san,d 
with  a  small  percentage  of  clay  or  loam  often  gives  better 
results  than  clean  sand.  Lean  mortar  may  be  improved  by 
adding  a  small  percentage  of  clay  or  loam,  or  by  using  dirty 
sand,  for  the  fine  material  increases  the  density.  In  rich  mor- 
tars this  is  not  needed,  as  the  cement  furnishes  all  the  fine 
material  necessary,  and  clay  or  loam  or  dirty  sand  might  prove 
detrimental.  Whether  it  is  really  a  benefit  or  not  depends 
chiefly  upon  the  richness,  of  the  concrete  and  the  coarseness  of 
the  sand.  Some  idea  of  the  cleanness  of  sand  may  be  obtained 
by  placing  it  in  the  palm  of  one  hand  and  rubbing  it  with  the 


REINFORCED  CONCRETE  9 

fingers  of  the  other.  If  the  sand  is  dirty  it  will  badly  discolor 
the  palm  of  the  hand.  When  it  is  found  necessary  to  use  dirty 
sand,  the  strength  of  the  concrete  should  be  tested. 

Sand  containing  loam  or  earthy  material  is  cleansed  by  wash- 
ing with  water,  either  in  a  machine  specially  designed  for  the 
purpose,  or  by  agitating  the  sand  with  water  in  boxes  provided 
with  holes  to  permit 'the  dirty  water  to  flow  away. 

Percentage  of  Voids.  As  before  stated,  a  mortar  is  strong- 
est when  composed  of  fine  and  coarse  grains  mixed  in  such  pro- 
portion that  the  percentage  of  voids  shall  be  the  least.  The 
simplest  method  of  comparing  two  sands  is  to  weigh  a  certain 
gross  volume  of  each,  the  sand  having  been  thoroughly  shaken 
down.  Assuming  that  the  stone  itself  of  each  kind  of  sand  has 
the  same  density,  then  the  heavier  volume  of  sand  will  have  the 
smaller  percentage  of  voids.  The  percentage  of  voids  in  packed 
sand  may  be  approximately  determined  by  measuring  the  vol- 
ume of  water  which  can  be  added  to  a  given  volume  of  the  sand. 
However,  if  the  water  is  poured  into  the  sand,  it  is  quite  cer- 
tain that  air  will  remain  in  the  voids  in  the  sand,  which  will  not 
be  dislodged  by  the  water,  and  the  apparent  volume  of  voids 
will  be  less  than  the  actual. 

The  precise  determination  of  the  percentage  of  voids  involves 
the  measurement  of  the  specific  gravity  of  the  stone  of  which 
the  sand  is  composed,  and  the  percentage  of  moisture  in  the 
sand,  all  of  which  is  done  with  elaborate  precautions.  Ordi- 
narily such  precise  determinations  are  of  little  practical  value, 
since  the  product  of  any  one  sand  bank  is  quite  variable. 
While  it  would  be  theoretically  possible  to  mix  fine  and  coarse 
sand,  varying  the  ratios  according  to  the  coarseness  of  the 
grains  as  obtained  from  the  sand  pit,  it  is  quite  probable  that 
an  over-refinement  in  this  particular  would  cost  more  than  the 
possible  saving  would  be  worth.  Sand  usually  has  from  28  to 
40  per  cent  of  voids.  An  experimental  test  of  sand  of  various 
degrees  of  fineness,  12^  per  cent  of  it  passing  a  No.  100  sieve, 
showed  only  22  per  cent  of  voids;  but  such  a  value  is  of  only 
theoretical  interest,  and  for  practical  operations  we  should 
assume  the  percentage  given  above. 


10  REINFORCED  CONCRETE 

BROKEN  STONE 

Classification  of  Stones.  The  term  broken  stone  ordinarily 
signifies  the  product  of  a  stone  crusher  or  the  result  of  hand- 
breaking-  by  hammering  large  blocks  of  stone;  but  the  term 
may  also  include  gravel,  described  below. 

The  best,  hardest,  and  most  durable  broken  stone  comes  from 
the  trap  rocks— dark,  heavy,  close-grained  rocks  of  igneous 
origin.  The  term  granite  is  usually  made  to  include  not  only 
true  granite,  but  also  gneiss,  mica  schist,  syenite,  etc.  These  are 
equally  good  for  concrete  work,  and  are  usually  less  expensive. 
Limestone  is  suitable  for  some  kinds  of  concrete  work;  but  its 
strength  is  not  so  great  as  that  of  granite  or  trap  rock,  and  it  is 
more  affected  by  a  conflagration.  Conglomerate,  often  called 
pudding  stone,  makes  a  very  good  concrete  stone.  The  value  of 
sandstone  for  concrete  varies  much  according  to  its  texture. 
Some  grades  are  very  compact,  hard,  and  tough,  and  make  a 
good  concrete ;  other  grades  are  friable,  and,  like  shale  and  slate, 
are  practically  unfit  for  use.  Gravel  consists  of  pebbles  of 
various  sizes,  produced  from  stones  which  have  been  broken 
up  and  then  been  worn  smooth  with  rounded  corners.  The  very 
fact  that ,  they  have  been  exposed  for  indefinite  periods  to 
atmospheric  disintegration  and  mechanical  wear  is  a  proof  of 
the  durability  and  mechanical  strength  of  the  stone. 

Sizes  of  Stones.  The  size  of  the  broken  stone  depends 
altogether  upon  the  use  to  be  made  of  the  concrete.  For  plain 
concrete  the  usual  size  is  2  inches.  The  maximum  size  is  never 
larger  than  2£  to  3  inches  and  the  minimum  is  seldom  less  than 
1J  inches.  Between  these  limits  the  size  is  dependent  largely 
upon  the  massiveness  of  the  work  to  be  constructed.  For  heavy 
walls,  foundations,  abutments,  etc.,  the  larger  stones  may  be 
used,  and  for  the  thin  walls,  arch  rings,,  etc.,  the  smaller  stones. 

In  reinforced  concrete  work  f-inch  and  1-inch  stones  are  gen- 
erally used.  The  smaller  size  is  to  be  preferred.  A  denser  and 
stronger  concrete  is  secured  by  using  graded  stone,  for  the 
smaller  stones  fill  in  between  the  larger  ones  and  less  mortar 
is  required.  For  reinforced  concrete  the  stones  should  vary 
from  i  inch  to  f  or  1  inch,  that  is,  the  run  of  crusher  may 


REINFORCED  CONCRETE  11 

be  used  between  these  limits ;  for  plain  concrete,  the  run  of  the 
crusher  may  be  used  between  the  limits  of  |  inch  and  2  or  3 
inches. 

The  amount  of  voids  in  broken  stone  of  uniform  size  is  about 
45  per  cent ;  this  is  true  whether  the  stone  is  \  inch  or  6  inches. 
To  secure  dense  concrete  it  is  necessary  to  have  these  voids 
filled.  A  simple  method  for  determining  the  amount  of  the 
voids  that  is  sufficiently  accurate  for  ordinary  work  has  been 
previously  described  for  obtaining  the  voids  in  sand.  If  the 
stone  is  slowly  dropped  into  the  water  there  is  much  less  danger 
of  error  due  to  air  bubbles  forming  on  the  stone,  than  if  the 
water  is  poured  into  a  vessel  which  contains  the  stone. 

Illustrative  Example.  A  cylinder  10  inches  in  diameter  and 
12  inches  deep  is,  say,  half  full  of  water,  and  into  it  stone  Is 
slowly  dropped  and  well  settled  until  the  vessel  is  level  full. 
The  stone  is  then  removed  and  the  depth  of  water  measured. 
Suppose  the  depth  of  water  is  found  to  be  5£  inches.  By 
dividing  the  volume  of  water  after  the  stones  have  been  re- 
moved by  the  volume  of  the  full  cylinder  we  shall  determine 
the  percentage  of  voids.  That  is: 

52  X  3.1416  X  12    =  942.48  cu.  in.,  volume  of  the  full 

cylinder 
52  X  3.1416  X    51  =  431.97  cu.  in.,  volume  of  water 

with  stones  removed 
431.97  -t-  942.48  =  45.7,  per  cent  of  voids 

Broken  stone  is  usually  sold  by  the  ton,  and  its  weight  varies 
from  2,200  to  3,200  pounds  per  cubic  yard.  Therefore  it  is 
necessary  to  know  how  much  stone  will  weigh  per  cubic  yard 
before  the  cost  of  concrete  can  be  accurately  figured. 

Slag.  Slag  is  now  being  used  in  some  sections  of  this 
country  for  reinforced  concrete  work  on  the  same  basis  as  trap 
rock  or  other  approved  stone.  Such  slag  must  be  air-cooled, 
blast-furnace  slag,  free  from  ashes  and  other  debris,  and  it 
should  weigh  at  leas.t  2,000  pounds  per  cubic  yard.  Water- 
cooled  slag  is  too  porous  to  be  used  for  the  higher  grades  of 
reinforced  concrete  work,  but  it  may  be  used  for  reinforced 


12  REINFORCED  CONCRETE 

concrete  slabs  supported  on  steel  beams  or  walls  at  a  higher 
value  than  1:2:4  cinder  concrete.  Slag  concrete  is  one  of  the 
best  fireproofing  materials  in  use. 

Cinders.  Cinders  for  concrete  should  be  free  from  coal 
and  soot.  Usually  a  better  mixture  can  be  obtained  by  screen- 
ing the  fine  stuff  from  the  cinders  and  then  mixing  in  a  larger 
proportion  of  sand,  than  by  using  unscreened  material,  although 
if  the  fine  stuff  is  uniformly  distributed  through  the  mass,  it 
may  be  used  without  screening  and  a  smaller  proportion  of 
sand  used. 

The  strength  of  cinder  concrete,  as  is  shown  later,  is  far 
less  than  that  of  stone  concrete;  and  on  this  account  it  can- 
not be  used  where  high  compressive  values  are  necessary.  But 
because  of  its  very  low  cost  compared  with  broken  stone,  espe- 
cially under  some  conditions,  it  is  used  rather  commonly  for 
roofs,  etc.,  on  which  the  loads  are  comparatively  small. 

One  possible  objection  to  the  use  of  cinders  often  advanced 
is  that  they  frequently  contain  sulphur  and  other  chemicals 
which  may  corrode  the  reinforcing  steel.  The  case  cited  on 
page  42  would  seem  to  refute  this  theory.  However,  in  any 
structure  where  the  strength  of  the  concrete  is  a  matter  of 
importance,  cinders  should  not  be  used  without  a  thorough 
inspection,  and  even  then  the  unit  compressive  values  allowed 
should  be  at  a  very  low  figure. 

MORTARS 

The  components  of  mortars  are  a  cementing  material,  sand, 
and  water.  The  cementing  material  may  be  either  lime  or 
cement;  often  both  are  used,  varying  in  proportion  to  suit  the 
character  of  the  work.  Mortar  made  with  lime  alone  as  the 
cementing  material  is  very  weak  and  is  seldom  used  except  for 
the  cheapest  work.  Portland  cement  is  always  used  when  the 
best  mortar  is  required,  either  alone  or  with  a  small  percentage 
of  lime.  Good  clean  sand  is  always  essential  in  making  mortar. 

Common  Lime  Mortar.  Lime  to  be  used  in  mortar  of  any 
kind  must  be  well  slaked  in  water-tight  boxes,  the  amount  of 
water  being  from  "2^  to  3  times  the  volume  of  the  unslaked 


REINFORCED  CONCRETE  13 

lime.  It  is  well  to  mix  one  part  of  the  slaked  lime  paste  with 
three  parts  sand.  Lime  mortar  is  used  only  for  cheap  work 
and  where  low  compressive  strength  is  required.  Brick  work 
constructed  with  lime  mortar  will  safely  support  a  load  of 
8  or  10  tons  per  square  foot. 

Natural  Cement  Mortar.  Mortar  made  with  natural  ce- 
ment is  little  used  except  in  sections  of  the  country  where 
natural  cement  is  made.  It  has  a  low  compressire  strength,  and 
is  slow  setting.  Mortar  made  with  natural  cement  should  never 
be  leaner  than  one  part  cement  to  three  parts  sand. 

Portland  Cement  Mortar.  Mortar  made  with  Portland 
cement  is  extensively  used.  It  is  usually  made  in  the  propor- 
tion of  one  part  of  Portland  cement  to  three  parts  sand,  when 
used  in  retaining  walls  and  other  work  of  a  similar  character. 
It  is  sometimes  mixed  in  the  proportions  of  1:2,  but  it  should 
never  be  made  richer  than  this,  for  in  exposed  places  the  excess 
of  cement  will  cause  it  to  crack.  This  mortar  is  also  mixed 
in  the  proportions  of  1 :  4  and  1 :  5,  depending  on  the  strength 
required.  Portland  cement  mortar  is  the  best  of  all  mortars 
used  in  building  construction,  is  reliable  in  all  climates,  not 
variable  in  bulk,  and  should  be  used  where  high  compressive 
strength  is  required.  Brickwork  laid  up  in  Portland  cement 
mortar  of  the  proportions  1 :  3  will  safely  support  a  load  of 
15  tons  per  square  foot,  and  rubble  stone  work  with  the  same 
mortar  will  support  10  tons  per  square  foot. 

Cement  Lime  Mortar.  This  mortar  varies  greatly  in  its 
composition.  A  small  amount  of  lime  is  often  added  to  a  Port- 
land cement  mortar  to  make  the  mortar  work  smoothly  or  a 
small  amount  of  Portland  cement  may  be  added  to  a  lime  mor- 
tar to  give  that  mortar  more  strength.  As  ordinarily  used, 
cement  lime  mortar  is  composed  of  one  part  Portland  cement, 
one  part  slaked  lime  paste,  and  four  parts  sand.  This  mor- 
tar has  fair  adhesive  power,  is  slow  to  set,  works  smoothly  and 
easily  with  the  trowel,  and  is  very  satisfactory  in  bonding 
brick  or  stone  in  the  walls  of  a  building.  Brickwork  con- 
structed with  this  mortar  will  safely  support  a  load  of  12  tons 
per  square  foot,  and  rubble  stone,  8  tons  per  square  foot. 


14  REINFORCED  CONCRETE 

CHARACTERISTICS    AND    PROPERTIES    OF    CONCRETE 
MIXTURES 

Principles  Used  in-  Proportioning  Concrete.  Theoretically, 
the  proportioning  of  the  sand  and  cementing  material  should 
be  done  by  weight.  This  is  always  the  method  in  laboratory 
testing.  The  volume  of  a  given  weight  of  cement  varies  greatly 
according  as  it  is  packed  or  loosely  thrown  in  a  pile.  This  is 
also  true  of  sand.  The  contents  of  a  barrel  of  Portland  cement 
will  increase  in  volume  from  10  to  30  per  cent  by  being  merely 
dumped  loosely  in  a  pile  and  then  shoveled  into  a  measuring 
box.  In  determining  the  proportions  for  concrete,  the  cement 
should  be  measured  in  the  packages  in  which  it  comes  from 
the  manufacturer,,  but  the  sand  and  stone  should  be  measure*] 
loose  as  they  are  thrown  in  the  measuring  boxes.  The  volume 
of  sand  also  depends  to  a  certain  extent  on  ii:s  condition.  Loose, 
dry  sand  occupies  a  considerably  larger  volume  than  wet  sand, 
and  this  is  still  more  the  case  when  the  sand  is  very  fine. 

Ideal  Conditions.  The  general  principle  to  be  adopted  is 
that  the  amount  of  water  should  be  just  sufficient  to  supply 
that  needed  for  crystallization  of  the  cement  paste;  that  the 
amount  of  paste  should  be  just  sufficient  to  fill  the  voids  be- 
tween the  particles  of  sand ;  that  the  mortar  thus  produced 
should  be  just  sufficient  to  fill  the  voids  between  the  broken 
stones.  If  this  ideal  could  be  realized  the  total  volume  of  the 
mixed  concrete  would  be  no  greater  than  that  of  the  broken 
stone.  But  no  matter  how  thoroughly  and  carefully  the  ingre- 
dients are  mixed  and  rammed,  the  particles  of  cement  will  get 
between  the  grains  of  sand  and  thus  cause  the  volume  of  the 
mortar  to  be  greater  than  that  of  the  sand ;  the  grains  of  sand 
will  get  between  the  smaller-  stones  and  separate  them ;  and  the 
smaller  stones  will  get  between  the  larger  stones  and  separate 
them.  Experiments*  by  Professor  I.  0.  Baker  show  that,  even 
when  the  volume  of  the  mortar  was  only  70  per  cent  of  the 
volume  of  the  voids  in  the  broken  stone,  the  volume  of  the 
rammed  concrete  was  5  per  cent  more  than  that  of  the  broken 
stone.  When  the  theoretical  amount  of  mortar  was  added,  the 
volume  was  7.5  per  cent  in  excess,  which  shows  that  it  is  prac- 


REINFORCED  CONCRETE  15 

tically  impossible  to  ram  such  concrete  and  wholly  prevent 
voids.  When  mortar  amounting  to  140  per  cent  of  the  voids 
was  used,  all  voids  were  apparently  filled,  but  the  volume  of 
the  concrete  was  114  per  cent  of  that  of  the  broken  stone. 

Conditions  in  Practice.  Therefore,  on  account  of  the  im- 
practicability of  securing  perfect  mixing,  the  amount  of  water 
used  is  always  somewhat  in  excess  (which  will  do  no  harm)  ; 
the  cement  paste  is  generally  made  somewhat  in  excess  of  that 
required  to  fill  the  particles  in  the  sand  (except  in  those  cases 
where,  for  economy,  the  mortar  is  purposely  made  very  lean)  ; 
and  the  amount  of  mortar  is  usually  considerably  in  excess  of 
that  required  to  fill  the  voids  in  the  stone.  Even  when  we  allow 
some  excess  in  all  the  ingredients,  there  is  so  much  variation 
in  the  percentage  of  voids  in  the  sand  and  broken  stone,  that 
not  only  does  the  best  work  require  an  experimental  determina- 
tion of  the  voids  in  the  materials  used,  but,  on  account  of  the 
liability  to  variation  in  those  percentages,  even  in  materials 
from  the  same  source  of  supply,  it  also  requires  a  constant 
testing  and  revision  of  the  proportions  as  the  work  proceeds. 
For  less  careful  work,  the  proportions  ordinarily  adopted  in 
practice  are  considered  sufficiently  accurate. 

Standard  Proportions.  On  the  general  principle  that  the 
voids  in  ordinary  broken  stone  are  somewhat  less  than  half  of 
the  volume,  it  is  a  very  common  practice  to  use  one-half  as 
much  sand  as  the  volume  of  the  broken  stone.  The  proportion 
of  cement  is  then  varied  according  to  the  strength  required  in 
the  structure,  and  according  to  the  desire  to  economize.  On  this 
principle  we  have  the  familiar  ratios  1:2:4,  1 :  2.5 :  5,  1 :  3 :  G, 
and  1:4:8.  It  should  be  noted  that  in  each  of  these  cases, 
in  which  the  numbers  give  the  relative  proportions  of  the 
cement,  sand,  and  stone,  respectively,  the  ratio  of  the  sand  to 
the  broken  stone  is  a  constant,  and  the  ratio  of  the  cement  is 
alone  variable,  for  it  would  be  equally  correct  to  express  the 
ratios  as  follows :  1 :  2  :  4,  0.8 :  2  :  4,  0.67 :  2 :  4,  0.5 :  2 :  4. 

Compressive  Strength.  The  compressive  strength  of  con- 
crete is  very  important,  as  concrete  is  used  more  often  in  com- 
pression than  in  any  other  way.  To  give  average  values  of  its 


16 


REINFORCED  CONCRETE 


TABLE  I 
Com  press!  ve  Strength  of  Concrete* 

(Tests  Made  at  Water-town  Arsenal,  1899) 


MIXTURE 

BRAND  OF  CEMENT 

STRENGTH  (Pounds  per  Square  Inch) 

7  Days 

1  Month 

3  Months 

6  Months 

1  :2  :4    j 
1  :3  :6    \ 

Saylor 
Atlas 
Alpha 
Germania 
Alsen 

Average 

Saylor 
Atlas 
Alpha 
Germania 
Alsen 

Average 

1,724 

1,387 
904 
2,219 
1.592 

2.238 
2.428 
2.420 
2,642 
2.269 

2,702 
2,966 
3,123 
3,082 
2,608 

3,510 
3,953 
4,411 
3,643 
3,612 

1,565 

2,399 

2,896 

3,826 

1,625 
1,050 
892 
1,550 
1,438 

2.568 
1,816 
2,150 
2,174 
2,114 

2,882 
1.538 
2,355 
2,486 
2,349 

3,567 
3,170 
2,750 
2,930 
3,026 

1,311 

2,164 

2,522 

3,088 

NOTE.— The  values  obtained  in  these  tests  are  exceedingly  high,  and 
cannot  be  safely  counted  on  in  practice. 

compressive  strength  is  rather  difficult,  as  that  is  dependent  on 
so  many  factors.  The  available  aggregates  are  so  varied,  and 
the  methods  of  mixing  and  manipulation  so  different,  that  tests 
must  be  studied  before  any  conclusions  can  be  drawn.  For 
extensive  work,  tests  should  be  made  with  the  materials  avail- 
able under  conditions  as  nearly  as  possible  like  those  of  the 
actual  structure. 

A  series  of  experiments  made  at  the  Watertown  Arsenal  for 
Mr.  George  A.  Kimball,  Chief  Engineer  of  the  Boston  Ele- 
vated Railway  Company,  in  1899,  was  one  of  the  best  sets  of 
tests  that  have  been  published,  and  the  results  are  given  in 
Table  I.  Portland  cement,  coarse,  sharp  sand,  and  stone  up  to 
2J  inches  were  used;  and  when  thoroughly  rammed,  the  water 
barely  flushed  to  the  surface. 

Tests  by  Professor  A.  N.  Talbotf  on  6-inch  cubes  of  con- 
crete, showed  the  average  values  given  in  Table  II.  The  cubes 
were  about  60  days  old  when  tested. 

*  From  Tests-  of  Metals,  1899. 

t  Bulletin  No.  14,  University  of  Illinois. 


REINFORCED  CONCRETE  17 

TABLE  II 
Compressive  Tests  of  Concrete 

(University  of  Illinois) 


No.  OF  TESTS 

MIXTURE 

STRENGTH  (Pounds  per 
Square  Inch) 

3 
6 

1:2:4 
1  :3  :5.5 
1:3:6 

2,350 
1,920 
1,300 

With  fair  conditions  as  to  the  character  of  the  materials  and 
workmanship,  a  mixture  of  1 :  2 : 4  concrete  should  show  a  com- 
pressive  strength  of  2,000  to  2,300  pounds  per  square  inch  in 
40  to  60  days ;  a  mixture  of  1 :  2.5 :  5  concrete,  a  strength  of 
1,800  to  2,000  pounds  per  square  inch ;  and  a  mixture  of  1 :  3 :  6 
concrete,  a  strength  of  1,500  to  1,800  pounds  per  square  inch. 
The  rate  of  hardening  depends  upon  the  consistency  and  the 
temperature. 

Tensile  Strength.  The  tensile  strength  of  concrete  is 
usually  considered  about  one-tenth  of  the  compressive  strength ; 
that  is,  concrete  which  has  a  compressive  value  of  2,000  pounds 
per  square  inch  should  have  a  tensile  strength  of  about  200 
pounds  per  square  inch.  Although  there  is  no  fixed  relation 
between  the  two  values,  the  general  law  of  increase  in  strength 
due  to  increase  in  the  percentage  of  cement  and  the  density 
seems  to  hold  in  both  cases. 

Shearing  Strength.  By  shearing  is  meant  the  strength  of 
the  material  against  a  sliding  failure  when  tested  as  a  rivet 
would  be  tested  for  shear.  The  shearing  strength  of  concrete 
is  important  on  account  of  its  intimate  relation  to  the  compres- 
sive strength  and  the  shearing  stresses  to  which  it  is  subjected 
in  structures  reinforced  with  steel.  Only  a  few  tests  have  been 
made,  as  they  are  rather  difficult ;  but  the  tests  made  show  that 
the  shearing  strength  is  nearly  one-half  the  crushing  strength. 

Modulus  of  Elasticity.  The  principal  use  of  the  modulus 
of  elasticity  in  designing  reinforced  concrete  is  in  determining 
the  relative  stresses  carried  by  the  concrete  and  the  steel.  The 
minimum  value  used  in  designing  reinforced  concrete  is  usually 
taken  as  2,000,000,  and  the  maximum  value  as  3,000,000,  de- 


18  REINFORCED  CONCRETE 

pending  on  the  richness  of  the  mixture  used.  For  ordinary 
concrete  a  value  of  2,500,000  is  generally  taken. 

Weight.  The  weight  of  stone  or  gravel  concrete  will  vary 
from  145  pounds  per  cubic  foot  to  155  pounds  per  cubic  foot, 
depending  upon  the  specific  gravity  of  the  materials  and  the 
degree  of  compactness.  The  weight  of  a  cubic  foot  is  usually 
considered  as  150  pounds. 

Cost.  The  cost  of  concrete  in  place  ranges  from  $4.50 
per  cubic  yard  to  $20,  or  even  $25,  per  cubic  yard,  varying 
chiefly  with  the  character  of  the  work  to  be  done,  and  the  condi- 
tions under  which  it  is  necessary  to  do  it.  The  cost  of  the  mate- 
rial, of  course,  will  always  have  to  be  considered,  but  this  is  not 
so  important  as  the  character  of  the  work.  When  concrete  is 
laid  in  large  masses,  so  that  the  expense  for  forms  is  relatively 
small,  the  cost  ranges  from  $4.50  per  cubic  yard  to  $6  or  $7 
per  cubic  yard,  depending  upon  the  local  conditions  and  cost 
of  materials.  Foundations  and  heavy  walls  are  good  examples 
of  this  class  of  work.  For  sewers  and  arches,  the  cost  varies 
from  $7  to  $13.  In  building  construction— floors,  roofs,  and 
thin  walls— the  cost  ranges  from  $14  to  $20  per  cubic  yard. 

Cement.  The  cost  of  Portland  cement  varies  with  the  de- 
mand. As  the  material  is  heavy,  the  freight  is  often  a  big  item. 
The  price  ranges  from  $1  to  $2  per  barrel,  and  to  this  must  be 
added  the  cost  of  handling. 

Sand.  The  cost  of  sand,  including  handling  and  freight,  is 
from  $0.75  to  $1.50  per  cubic  yard;  a  common  price  for  sand 
delivered  in  the  cities  is  $1  per  cubic  yard. 

Broken  Stone  or  Gravel.  The  cost  of  broken  stone  delivered 
in  the  cities  varies  from  $1.25  to  $1.75  per  cubic  yard.  The  cost 
of  gravel  is  usually  a  little  less. 

Mixing.  Under  ordinary  conditions  and  where  the  concrete 
must  be  wheeled  only  a  very  short  distance,  the  cost  of  hand- 
mixing  and  placing  generally  ranges  from  $0.90  to  $1.30  per 
cubic  yard,  if  done  by  men  skilled  in  this  work.  If  a  mixer  is 
used,  the  cost  is  from  $0.50  to  $0.90  per  cubic  yard. 

Forms.  The  cost  of  forms  for  heavy  walls  and  foundations 
varies  from  $0.70  to  $1.20  per  cubic  yard  of  concrete  laid. 


REINFORCED  CONCRETE  19 

These  last  two  items — the  cost  of  forms  and  mixing — are  dis- 
cussed later. 

Variations  from  Standard  Aggregate 

In  the  previous  discussions  the  standard  aggregate  composed 
of  broken  stone  or  gravel  has  been  assumed.  There  are  two 
other  types  of  concrete,  cinder  and  rubble,  which  are  used  under 
certain  circumstances. 

Cinder  Concrete.  Cinder  concrete  has  been  used  to  some 
extent  on  account  of  its  light  weight.  The  strength  of  cinder 
concrete  is  from  one-third  to  one-half  the  strength  of  stone  con- 
crete. It  weighs  about  110  pounds  per  cubic  foot. 

Rubble  Concrete.  Advantages.  Rubble  concrete  includes 
any  class  of  concrete  in  which  large  stones  are  placed.  The 
chief  use  of  this  concrete  is  in  constructing  dams,  lock-walls, 
breakwaters,  retaining  walls,  and  bridge  piers. 

The  cost  of  rubble  concrete  in  large  masses  should  be  less  than 
that  of  ordinary  concrete,  as  the  expense  of  crushing  the  stone 
used  as  rubble  is  saved,  and  as  each  large  stone  replaces  a  por- 
tion of  cement  and  aggregate,  that  portion  of  cement  is  saved, 
as  well  as  the  labor  of  mixing  it.  The  weight  of  a  cubic  foot 
of  stone  is  greater  than  that  of  an  equal  amount  of  ordinary 
concrete,  because  of  the  pores  in  the  concrete;  the  rubble  con- 
crete is  therefore  heavier,  which  increases  its  value  for  certain 
classes  of  work.  Rubble  concrete  is  generally  found  to  be 
cheaper  than  rubble  masonry,  because  it  requires  very  little 
skilled  labor,  but  for  walls  3  or  3i  feet  thick,  the  rubble 
masonry  is  usually  cheaper,  owing  to  the  saving  in  forms. 

Proportion  and  Size  of  Stone.  Usually  the  proportion  of 
rubble  stone  is  expressed  in  percentage  of  the  finished  work, 
varying  from  20  to  65  per  cent.  The  percentage  depends  largely 
on  the  size  of  the  stone  used,  as  there  must  be  nearly  as  much 
space  left  between  small  stones  as  between  large  ones.  The 
percentage  therefore  increases  with  the  size  of  the  stones. 
When  "one-man"  or  "tw7o-man"  rubble  stone  is  used,  about  20 
per  cent  to  25  per  cent  of  the  finished  work  is  composed  of 
these  stones.  When  the  stones  are  large  enough  to  be  handled 
with  a  derrick,  the  proportion  is  increased  to  about  33  per  cent; 


20  REINFORCED  CONCRETE 

and  to  55  per  cent,  or  even  65  per  cent,  when  the  stones  average 
from  1  to  2-1  cubic  yards  each. 

The  distance  between  the  stones  may  vary  from  3  inches  to  15 
or  18  inches.  With  a  very  wet  mixture  of  concrete,  which  is 
generally  used,  the  stones  can  be  placed  much  closer  than  if  a 
dry  mixture  is  used.  With  the  latter  mixture,  the  space  must 
be  sufficient  to  allow  the  concrete  to  be  thoroughly  rammed 
into  all  of  the  crevices.  Specifications  often  state  that  no 
rubble  stone  shall  be  placed  nearer  the  surface  of  the  concrete 
than  6  to  12  inches. 

Rubble  Masonry  Faces.  The  faces  of  dams  are  very  often 
built  of  rubble,  ashlar,  or  cut  stone,  and  the  filling  between  the 
faces  made  of  rubble  concrete.  For  this  style  of  construction, 
no  forms  are  required.  For  nibble  concrete,  when  the  faces  are 
not  constructed  of  stone,  wooden  forms  are  constructed  as  for 
ordinary  concrete. 

Comparison  of  Quantities  of  Materials.  The  mixture  of  con- 
crete used  for  this  class  of  work  is  often  1  part  Portland 
cement,  3  parts  sand,  and  6  parts  stone.  The  quantities  of 
materials  required  for  one  yard  of  concrete,  according  to  Table 
VI,  are  1.05  barrels  cement,  0.44  cubic  yard  sand,  and  0.88 
cubic  yard  stone.  If  rubble  concrete  is  used,  and  if  the  rubble 
stone  laid  averages  0.40  cubic  yard  for  each  yard  of  concrete, 
then  40  per  cent  of  the  cubic  contents  is  rubble,  and  each  of  the 
other  materials  may  be  reduced  40  per  cent.  The  proportions 
for  one  cubic  yard  would  then  be :  1.05  X  0.60  =  0.63  barrel  of 
cement ;  0.44  X  0.60  =  0.26  cubic  yard  sand ;  and  0.88  X  0.60  = 
0.53  cubic  yard  stone. 

A  dam  on  the  Quinebaug  River  is  a  good  example  of  rubble- 
concrete  construction.  The  height  of  the  dam  varies  from  30 
to  45  feet  above  bedrock.  In  making  the  concrete  there  were 
used  the  bank  sand  and  gravel  excavated  from  the  bars  in  the 
bed  of  the  river,  arid  the  rock  and  boulders  of  varying  sizes 
taken  from  the  site  of  the  dam.  Stones  containing  2  to  2* 
cubic  yards  were  used  in  the  bottom  of  the  dam,  but  in  the 
upper  part  of  the  dam  smaller  stones  were  placed.  The  total 
amount  of  concrete  used  in  the  dam  was  about  12,000  cubic 


REINFORCED  CONCRETE  21 

yards,  there  being  14  cubic  yards  of  concrete  for  each  barrel 
of  cement  used.  The  concrete  was  mixed  wet,  and  the  large 
stones  were  so  placed  that  no  voids  or  hollows  would  exist  in 
the  finished  work. 

MIXING  AND  LAYING  CONCRETE 
Methods  of  Proportioning 

Rich  Mixture.  A  rich  mixture,  proportions  1:2:4  —  that  is, 
1  barrel  (4  bags)  packed  Portland  cement  (as  it  comes  from 
the  manufacturer),  2  barrels  (7.6  cubic  feet)  loose  sand,  and  4 
barrels  (15.2  cubic  feet)  loose  stone— is  used  in  arches,  rein- 
forced concrete  floors,  beams,  and  columns  for  heavy  loads; 
engine  and  machine  foundations  subject  to  vibration;  tanks; 
and  for  water-tight  work. 

Medium  Mixture.  A  medium  mixture,  proportions  1 :  2.5 :  5 
—that  is,  1  barrel  (4  bags)  packed  Portland  cement,  2^  barrels 
(9.5  cubic  feet)  loose  sand,  and  5  barrels  (19  cubic  feet)  loose 
gravel  or  stone— may  be  used  in  arches,  thin  walls,  floors, 
beams,  sewers,  sidewalks,  foundations,  and  machine  founda- 
tions. 

Ordinary  Mixture.  An  ordinary  mixture,  proportions 
1:3:  6— that  is,  1  barrel  (4  bags)  packed  Portland  cement,  3 
barrels  (11.4  cubic  feet)  loose  sand,  and  6  barrels  (22.8  cubic 
feet)  loose  gravel  or  brqken  stone— may  be  used  for  retaining 
walls,  abutments,  piers,  and  machine  foundations. 

Lean  Mixture.  A  lean  mixture,  proportions  1:4:8  —  that  is, 
1  barrel  (4  bags)  packed  Portland  cement,  4  barrels  (15.2  cubic 
feet)  loose  sand,  and  8  barrels  (30.4  cubic  feet)  loose  gravel  or 
broken  stone— may  be  used  in  large  foundations  supporting 
stationary  loads,  backing  for  stone  masonry,  or  where  the  con- 
crete is  subject  to  a  low  compressive  load. 

Tendency  toward  Richer  Mixtures.  These  proportions 
must  not  be  taken  as  being  always  the  most  economical,  but 
they  represent  average  practice.  Cement  is  the  most  expensive 
ingredient ;  therefore  a  reduction  of  the  quantity  of  cement, 
by  adjusting  the  proportions  of  the  aggregate  so  as  to  produce 
a  concrete  with  the  same  density,  strength,  and  impermeability, 


22 


REINFORCED  CONCRETE 


TABLE  III* 
Proportions  of  Cement,  Sand,  and  Stone  in  Actual  Structures 


STRUCTURE 

PROPORTIONS 

REFERENCE 

C.  B.  &Q.  R.  R. 

Reinforced  Concrete  Culverts  

Phila.  Rapid  Transit,  Co. 
Floor  Elevated  Roadway 

1:3:6 
1:3:6 

Engr.  Cont.,  Oct.  3,  '06 
Sept  26  '06 

^SSi::::::::::::::::::::: 

C.  P.  R.  R. 

Arch  Rings 

1:2.5:5 
1:3:6 

1:3:5 

Piers  and  Abutments  

Hudson  River  Tunnel  Caisson  
Stand  Pipe  at  Attleboro,  Mass  
Height,  106  feet. 

C.  C.  &  St.  L.  R.  R.,  Danville  Arch 
Footings  

1:4:7 

1:2:4 
1:2:4 

1:4:8  or  1:9.5 

Cement  Era,  Aug.  '06 

Eng.  Record,  Sept.  29,  '06 
„      29,  '06 

March  3,  '06 

Arch  Rings  
Abutments,  Piers  

N.  Y.  C.  &  H.  R.  R.  R. 

Ossining    [Footing 

1:2:4 
1:3:6  or  1:6.5 

1:4:7.5 

3,  '06 

Tunnel     {Walls  
[Coping 

1:3:6 
1:2:4 

American  Oak  Leather  Co. 
Factory  at  Cincinnati,  Ohio  

1:2:4 

.        3,  '03 

harvard  University  Stadium  

few  York  Subway 
Roofs  and  Sidewalks 

1:3:6 
1:2:4 

Tunnel  Arches  
Wet  Foundation  2  ft.  th.  or  less  
„              „           exceeding  2  ft  

Boston  Subway             

1:2.5:5 
1:2:4 
1:2.5:5 

1:2.5:4 

P.  &  R.  R.  R. 

Arches 

1:2:4 

Oct.  13,  '06 

Piers  and  Abutments  

Brooklyn  Navy  Yd.  Laboratory 
Columns  
Beams  and  Slabs  

1:3:6 

1:2:3  Trap  rock 
1:3:5    „ 

Eng.  News,  March  23,  '05 

Roof  Slab  

Southern  Railway 
Arches  
Piers  and  Abutments  

1:3:5  Cinder 

1:2:4 
1:2.5:5 

is  of  great  importance.  By  careful  proportioning  and  work- 
manship, water-tight  concrete  has  been  made  of  a  1:3:6 
mixture. 


*  Tables  III  to  VII  have  been  taken  from  Gillette's  Handbook  of  Cost 
Data. 


REINFORCED  CONCRETE 


23 


TABLE  IV 

Barrels  of  Portland  Cement  per  Cubic  Yard  of  Mortar 

(Voids  in  sand  being  35  per  cent,  and  1  barrel  cement  yielding  3.65  cubic 
feet  of  cement  paste) 


PROPORTION  OP  CEMENT  TO  SAND 

1:1 

1:1.5 

1:2 

1:2.5 

1:3 

1:4 

Bbl.  specified  to  be  3.5  cu.  ft.  .  . 

»         »             »      3  8      „ 

Bbls. 
4.22 
4  09 

Bbls. 
3.49 

0      00 

Bbls. 
2.97 
2  81 

Bbls. 
2.57 
2  45 

Bbls. 

2.28 
2  16 

Bbls. 

1.76 
1  62 

.      4.0      „     

4.00 
3  81 

3.24 
3  07 

2.73 
2  57 

2.36 
2  27 

2.08 
2  00 

1.54 
1  40 

»             »                  n                      » 

Cu.  yds.  sand  per  cu.  yd.  mortar  

0.6 

0.7 

0.8 

0.9 

1.0 

1.0 

In  the  last  few  years  the  tendency  throughout  the  country 
has  been  to  use  a  richer  mixture  than  formerly  for  reinforced 
concrete.  The  1:2:4  mixture  is  now  employed  for  practically 
all  buildings  constructed  of  reinforced  concrete,  even  if  low 
stresses  are  used,  although  theoretically  a  1 :  2.5 :  5  mixture 
should  have  sufficient  strength. 

In  Table  III  will  be  found  the  proportions  of  the  concrete 
used  in  various  well-known  structures  and  in  Tables  IV  to  VII 
the  amounts  of  materials  used  per  cubic  yard  for  the  different 
proportions. 

Proper  Proportions  Determined  by  Trial.  An  accurate 
and  simple  method  to  determine  the  proportions  of  concrete 
is  by  trial  batches.  The  apparatus  consists  of  a  scale,  and  a 
cylinder  which  may  be  a  piece  of  wrought-iron  pipe  10  inches 
to  12  inches  in  diameter  capped  at  one  end.  Measure  and  weigh 
the  cement,  sand,  stone,  and  water,  and  mix  on  a  piece  of  sheet 
steel,  the  mixture  being  of  the  same  consistency  as  that  to  be 
used  in  the  work.  Place  the  mixture  in  the  cylinder,  carefully 
tamp  it,  and  note  the  height  to  which  the  pipe  is  filled.  The 
pipe  should  be  weighed  before  and  after  being  filled  so  as  to 
check  the  weight  of  the  material.  The  cylinder  is  then  emptied 
and  cleaned.  Mix  up  another  batch  of  the  same  weight,  using 
the  same  amount  of  cement  and  water,  but  slightly  varying  the- 
ratio  of  the  sand  and  the  stone.  Put  the  mixture  in  the  cylinder 
as  before  and  note  its  height.  Several  trials  should  be  made 
until  the  mixture  is  found  which  gives  the  least  height  in  the 


24 


REINFORCED  CONCRETE 


TABLE  V 

Barrels  of  Portland  Cement  per  Cubic  Yard  of  Mortar 

(Voids  in  sand  being  4,r»  per  cent  and  1  barrel  cement  yielding  3.4  cubic 
feet  of  cement  paste) 


PROPORTION  OF  CEMENT  TO  SAND 

1:1 

1:1.5 

1:2 

1:2.5 

1:3 

1:4 

Bbl.  specified  to  be  3.5  cu.  ft  
3  8 

Bbls. 

4.62 
4  32 

Bbls. 
3.80 
3  61 

Bbls. 
3.25 
3  10 

Bbls. 

2.84 
2  72 

Bbls. 
2.35 
2  16 

Bbls. 
1.76 
1  62 

.          1             „      4.0      .     
,          "             "44" 

4.19 
3  94 

3.46 
3  34 

3.00 
2  90 

2.64 
2  57 

2.05 
1  86 

1.54 
1  40 

Cu.  yds.  sand  per  cu.  yds.  mortar  

0.6 

0.8 

0.9 

1.0 

1.0 

1.0 

cylinder,  and  at  the  same  time  works  well  while  mixing,  all  the 
stones  being  covered  with  mortar,  and  which  makes  a  good 
appearance.  This  method  gives  good  results,  but  it  does  not 
indicate  the  various  sizes  of  the  sand  and  stone  to  use  to  secure 
the  most  economical  composition,  as  would  be  shown  in  a  thor- 
ough mechanical  analysis. 

There  has  been  much  concrete  work  done  where  the  propor- 
tions were  selected  without  any  reference  to  voids,  which  has 
given  much  better  results  in  practice  than  might  be  expected. 
The  proportion  of  cement  to  the  aggregate  depends  upon  the 
nature  of  the  construction  and  the  required  degree  of  strength 
and  water-tightness,  as  well  as  upon  the  character  of  the  inert 

TABLE  VI 
Ingredients  in  1  Cubic  Yard  of  Concrete 

(Sand  voids,  40  per  cent;  stone  voids,  45  per  cent;   Portland  cement, 

barrel  yielding  3.6f>  cubic  feet  paste  :  barrel  specified 

to  be  3.8  cubic  feet) 


PROPORTIONS  BY  VOLUME 

1:2:4 

1:2:5 

1:2:6 

1:2.5:5 

1:2.5:6 

1:3:4 

1.25 
0.53 
0.71 

1:4:9 

Bbls.  cement  per  cu.  yd.  concrete  
Cu.  yds.  sand             „           „          
„        stone            „           „          

1.46 
0.41 

0.82 

1.30 
0.36 
0.90 

1.18 
0.33 
1,00 

1.13 
0.40 
0  80 

1.00 
0.35 
0  84 

Proportions  by  volume  

1:3:5 

1:3:6 

1:3:7 

1:4:7 

1:4:8 

Bbls.  cement  per  cu.  yd.  concrete  
Cu.  yds.  sand             „           „          
„        stone            „            „ 

1.13 
0.48 
0.80 

1.05 
0.44 
0.88 

0.96 
0.40 
0.93 

0.82 
0.46 
0.80 

0  77 
0.43 
0.86 

0.73 
0.41 
0.92 

- — This  table  is  to  be  used  when  cement  is  measured  packed  in 
the  barrel,  for  the  ordinary  barrel  holds  3.8  cubic  feet. 


REINFORCED  CONCRETE  25 

TABLE  VII 

Ingredients  in  1  Cubic  Yard  of  Concrete 

(Sand  voids,  40  per  cent;  stone  voids,  45  per  cent;  Portland  cement, 

barrel  yielding  3.65  cubic  feet  paste  :  barrel  specified 

to  be  4.4  cubic  feet) 


PROPORTIONS  BY  VOLUME 

1:2:4 

1:2:5 

1:2:6 

1:2.5:5 

1:2.5:6 

1:3:4 

Bbls  cement  oer  cu  yd  concrete 

1  30 

1  16 

1  00 

1  07 

0  96 

1.08 

Cu.  yds.  sand             *           n          

0.42 

0.38 

0.33 

0.44 

0.40 

0.53 

„        stone            „           „          

0.84 

0.95 

1.00 

0.88 

0.95 

0.71 

Proportions  by  volume  

1:3:5 

1:3:6 

1:3:7 

1:4:7 

1:4:8 

1:4:9 

Bbls.  cement  per  cu.  yd.  concrete  
Cu.  yds.  sand             „           „          

0.96 
0.47 

0.90 
0.44 

0.82 
0.40 

0.75 
0.49 

0.68 
0.44 

0.64 
0.42 

„        stone            „            „          

0.78 

0.88 

0.93 

0.86 

0.88 

•0.95 

NOTE. — This  table  is  to  be  used  when  the  cement  is  measured  loose, 
after  dumping  it  into  a  box,  for  under  such  conditions  a  barrel  of  cement 
yields  4.4  cubic  feet  of  loose  cement. 

materials,  both  strength  and  imperviousness  being  increased 
with  a  larger  proportion  of  cement.  Richer  mixtures  are  nec- 
essary for  loaded  columns,  beams  in  building  construction,  and 
arches,  for  thin  walls  subject  to  water  pressure,  and  for  foun- 
dations laid  under  water.  The  actual  measurements  of  mate- 
rials as  mixed  and  used  usually  show  leaner  mixtures  than  the 
nominal  proportions  specified.  This  is  largely  due  to  the  heap- 
ing of  the  measuring  boxes. 


Wetness  of  Concrete 

In  regard  to  plasticity,  or  facility  for  working  and  molding, 
concrete  may  be  divided  into  three  classes:  dry,  medium,  and 
very  wet. 

Dry  Concrete.  Dry  concrete  is  used  in  foundations  which 
may  be  subjected  to  severe  compression  a  few  weeks  after  the 
concrete  is  laid.  It  should  not  be  placed  in  layers  of  more  than 
8  inches,  and  should  be  thoroughly  rammed.  In  a  dry  mixture 
the  water  will  just  flush  to  the  surface  only  when  it  is  thor- 
oughly tamped.  A  dry  mixture  sets  and  will  support  a  load 
much  sooner  than  will  a  wetter  mixture,  and  it  generally  is 
used  only  where  the  load  is  to  be  applied  soon  after  the  con- 
crete is  placed.  The  mixture  requires  the  exercise  of  more  than 


26  REINFORCED  CONCRETE 

ordinary  care  in  ramming,  as  pockets  are  likely  to  form  in  the 
concrete.  One  argument  against  it  is  the  difficulty  of  getting  a 
uniform  product. 

Medium  Concrete.  Medium  concrete  will  quake  when 
rammed,  and  has  the  consistency  of  liver  or  jelly.  It  is  adapted 
for  construction  work  suited  to  the  employment  of  mass  con- 
crete, such  as  retaining  walls,  piers,  foundations,  arches,  abut- 
ments; sometimes  it  is  also  employed  for  reinforced  concrete. 

Very  Wet  Concrete.  A  very  wet  mixture  of  concrete  will 
run  off  a  shovel  unless  it  is  handled  very  quickly,  and  an  ordi- 
nary rammer  will  sink  into  it  of  its  own  weight.  This  mixture 
is  suitable  for  reinforced  concrete  construction,  such  as  thin 
walls,  floors,  columns,  tanks,  and  conduits. 

Modern  Practice.  Within  the  last  few  years  there  has  been 
a  marked  change  in  the  amount  of  water  used  in  mixing  con- 
crete. The  dry  mixture  has  been  superseded  by  a  medium  or 
very  wet  mixture,  often  one  so  wet  as  to  require  no  ramming 
whatever.  Experiments  have  shown  that  dry  mixtures  give  bet- 
ter results  in  short  time  tests  and  wet  mixtures  in  long  time 
tests.  Some  experiments  made  on  dry,  medium,  and  wet  mix- 
tures showed  that  the  medium  mixture  was  the  most  dense,  wet 
next,  and  dry  the  least.  The  experimenter  concluded  that  the 
medium  mixture  is  the  most  desirable,  since  it  will  not  quake  in 
handling  but  will  quake  under  heavy  ramming.  He  found 
medium  1  per  cent  denser  than  wet  concrete  and  9  per  cent 
denser  than  dry  concrete;  he  considers  thorough  ramming  im- 
portant. 

Concrete  is  often  used  so  wet  that  it  will  not  only  quake  but 
flow  freely,  and  after  setting  it  appears  to  be  very  dense  and 
hard.  Some  engineers  think  that  the  tendency  is  to  use  far  too 
much  rather  than  too  little  water,  and  that  thorough  ramming 
is  desirable.  In  thin  walls  very  wet  concrete  can  be  more  easily 
pushed  from  the  surface  so  that  the  mortar  can  get  against  the 
forms  and  give  a  smooth  surface.  It  has  also  been  found  essen- 
tial that  the  concrete  should  be  wet  enough  to  flow  under  and 
around  the  steel  reinforcement  so  as  to  secure  a  good  bond 
between  the  steel  and  concrete. 


REINFORCED  CONCRETE  27 

Following  are  the  specifications  (1903)  of  the  American  Rail- 
way Engineering  and  Maintenance  of  Way  Association : 

The  concrete  shall  be  of  such  consistency  that  when  dumped  in  place 
it  will  not  require  tamping  ;  it  shall  be  spaded  down  and  tamped  suffi- 
ciently to  level  off  and  will  then  quake  freely  like  jelly,  and  be  wet 
enough  on  top  to  require  the  use  of  rubber  boots  by  workmen. 

Methods  of  Mixing 

Characteristics.  The  method  of  mixing  concrete  is  imma- 
terial, if  a  homogeneous  mass,  containing  the  cement,  sand,  and 
stone  in  the  correct  proportion,  is  secured.  The  value  of  the 
concrete  depends  greatly  upon  the  thoroughness  of  the  mixing. 
The  color  of  the  mass  must  be  uniform,  and  each  grain  of  sand 
and  piece  of  the  stone  should  have  cement  adhering  to  every 
point  of  its  surface. 

Two  methods  are  used  in  mixing  concrete— by  hand  and  by 
machinery.  Good  concrete  may  be  made  by  either  method  and 
in  both  cases  the  concrete  should  be  carefully  watched  by  a 
good  foreman.  If  a  large  quantity  of  concrete  is  required,  it 
is  cheaper  to  mix  it  by  machinery.  On  small  jobs  where  the 
ratio  of  the  cost  of  erecting  the  plant,  together  with  the  interest 
and  depreciation,  to  the  number  of  cubic  yards  to  be  made, 
is  large,  or  if  frequent  moving  is  required,  it  is  very  often 
cheaper  to  mix  the  concrete  by  hand.  The  relative  cost  of  the 
two  methods  usually  depends  upon  circumstances,  and  must  be 
worked  out  in  each  individual  case. 

Mixing  by  Hand.  The  placing  and  handling  of  materials 
and  the  arrangement  of  the  plant  are  varied  by  different 
engineers  and  contractors.  The  mixing  of  concrete  is  in 
general  a  simple  operation,  but  it  should  be  carefully  watched 
by  an  inspector.  He  must  attend  to  the  following  details: 

(1)  That  the  exact  amount  of  stone  and  sand  are  measured  out 

(2)  That  the  cement  and  sand  are  thoroughly  mixed 

(3)  That  the  mass  is  thoroughly  mixed 

(4)  That  the  proper  amount  of  water  is  used 

(5)  That  care  is  taken  in  dumping  the  concrete  in  place 

(6)  That  it  is  thoroughly  rammed 

Mixing-Platform.  The  mixing-platform,  which  is  usually  10 
to  20  feet  square,  is  made  of  1-inch  or  2-inch  plank  planed  on 


28  REINFORCED  CONCRETE 

one  side  and  well  nailed  to  stringers;  it  should  be  placed  as 
near  the  work  as  possible,  but  so  situated  that  the  stone  can 
be  dumped  on  one  side  of  it  and  the  sand  on  the  opposite  side. 
A  very  convenient  way  to  measure  the  stone  and  sand  is  by 
the  means  of  bottomless  boxes.  These  boxes  are  of  such  a 
size  that  they  hold  the  proper  proportions  of  stone  or  sand  to 
mix  a  batch  of  a  certain  amount.  Cement  is  usually  measured 
by  the  package,  that  is,  by  the  barrel  or  bag,  as  each  contains 
a  definite  amount  of  cement. 

Process  of  Mixing.  The  method  used  for  mixing  the  con- 
crete has  little  effect  upon  its  strength,  if  the  mass  has  been 
turned  a  sufficient  number  of  times  thoroughly  to  mix  the 
ingredients.  One  of  the  following  five  methods  is  generally 
used:* 

(1)  Cement    and    sand    mixed    dry    and    shoveled    on    the    stone    or 
gravel,  leveled  off,  and  wet  as  the  mass  is  turned 

(2)  Cement  and  sand   mixed   dry,  the  stone  measured  and  dumped 
on  top  of  it,  leveled  off,  and  wet,  as  turned  with  shovels 

(3)  Cement  and  sand  mixed  into  a  mortar,  the  stone  placed  on  top 
of  it  and  the  mass  turned 

(4)  Cement  and    sand   mixed    with    water   into   a   mortar   which   is 
shoveled  on  the  gravel  or  stone  and  the  mass  turned  with  shovels 

(5)  Stone  or  gravel,  sand,  and  cement  spread  in  successive  layers, 
hiixed  slightly  and  shoveled  into  a  mound,  water  poured  into  the  cen- 
ter, and  the  mass  turned  with  shovels 

The  quantity  of  water  is  regulated  by  the  appearance  of  the 
concrete.  The  best  method  of  wetting  the  concrete  is  by  meas- 
uring the  water  in  pails.  This  insures  a  more  nearly  uniform 
mixture  than  spraying  the  mass  with  a  hose. 

Mixing  by  Machinery.  On  large  contracts  the  concrete  is 
generally  mixed  by  machinery.  The  economy  is  not  only  in  the 
mixing  itself  but  in  the  appliances  introduced  in  handling  the 
raw  materials  and  the  final  product.  If  all  materials  are  deliv- 
ered to  the  mixer  in  wheelbarrows,  and  if  the  concrete  is  con- 
veyed away  in  wheelbarrows,  the  cost  of  making  concrete  is 
high,  even  if  machine  mixers  are  used.  If  the  materials  are 
fed  from  bins  by  gravity  into  the  mixer,  and  if  the  concrete 


*From  Taylor  and  Thompson's  Concrete. 


REINFORCED  CONCRETE 


TABLE  VIII 
Tensile  Tests  of  Concrete* 

(The  mixture  tested  being  composed  of  1  part  cement  and  10.18  parts 
aggregate) 


STRENGTH    (Pounds  per  Square  Inch) 

AGE  AND  METHOD  or 

MIXING 

High 

Low 

Average 

Aye  7  Dans 

Machine-mixed  sample 

260 

243 

253 

llnnd-mixed  sample 

159 

113 

134 

Aye  28  Days 

Machine-mixed  sample 

294 

249 

274 

Hand-mixed  sample 

231 

197 

211 

Age  6  Months 

Machine-mixed  sample 

441 

345 

388 

Hand-mixed  sample 

355 

298 

324 

Atje  One  Year 

Machine-mixed  sample 

435 

367 

391 

Hand-mixed  sample 

3«59 

312 

343 

*  From  H.  A.  Reid's  Concrete  and  Reinforced  Concrete  Construction. 

is  dumped  from  the  mixer  into  cars  and  hauled  away,  the  cost 
of  making  the  concrete  should  be  very  low. 

Machine  vs.  Hand  Mixing.  It  has  already  been  stated  that 
good  concrete  may  be  produced  by  either  machine  or  hand 
mixing,  if  it  is  thoroughly  mixed. 

Tests  made  by  the  U.  S.  government  engineers  at  Duluth, 
Minnesota,  to  determine  the  relative  strength  of  cor.crete  mixed 
by  hand  and  concrete  mixed  by  machine  (a  cube  mixer), 
showed  that  at  7  days,  hand-mixed  concrete  possessed  only  53 
per  cent  of  the  strength  of  the  machine-mixed  concrete;  at  28 
days,  77  per  cent;  at  6  months,  84  per  cent;  and  at  one  year, 
88  per  cent.  Details  of  these  tests  are  given  in  Table  VIII. 

It  should  be  noted  in  this  connection,  that  the  variations  in 
strength  were  greatest  in  the  hand-mixed  samples,  and  that 
the  strength  was  more  nearly  uniform  in  the  machine-mixed. 

Problems  in  Laying  Concrete 

Transporting  and  Depositing  Concrete.  Concrete  is  usually 
deposited  in  layers  of  0  inches  to  12  inches  in  thickness.  In 
handling  and  transporting,  care  must  be  taken  to  prevent  the 
separation  of  the  stone  from  the  mortar.  The  usual  method 


30  REINFORCED  CONCRETE 

of  transportation  is  by  wheelbarrows,  although  the  concrete  is 
often  handled  by  cars  and  carts,  and  on  small  jobs  it  is  some- 
times carried  in  buckets.  A  common  practice  is  to  dump  it 
from  a  height  of  several  feet  into  a  trench.  Many  engineers 
object  to  this,  claiming  that  the  heavy  and  light  portions  sep- 
arate while  falling  and  that  the  concrete  is  therefore  not 
uniform  through  its  mass;  they  insist  that  the  concrete  must 
be  gently  slid  into  place.  A  wet  mixture  is  much  more  easily 
handled  than  a  dry  mixture,  for  the  stone  will  not  so  readily 
separate  from  the  mass.  A  very  wet  mixture  has  been  deposited 
from  the  top  of  forms  43  feet  high  and  the  structure  was 
found  to  be  waterproof.  On  the  other  hand,  the  stones  in  a 
dry  mixture  will  separate  from  the  mortar  on  the  slightest 
provocation.  Where  it  is  necessary  to  drop  a  dry  mixture 
several  feet,  it  should  be  done  by  means  of  a  chute  or  pipe. 

Ramming  Concrete.  Immediately  after  concrete  is  placed, 
it  should  be  rammed  or  puddled,  care  being  taken  to  force  out 
the  air  bubbles.  The  amount  of  ramming 
necessary  depends  upon  the  amount  of  water 
used  in  the  mixing.  If  a  very  wet  mixture  is 
used,  there  is  danger  of  too  much  ramming, 
which  would  result  in  wedging  the  stones  to- 
gether and  forcing  the  cement  and  sand  to  the 
surface.  The  chief  object  in  ramming  a  very 
wet  mixture  is  simply  to  expel  the  bubbles 
of  air. 

The  style  of  rammer  ordinarily  used  depends 
on  whether  a  dry,  medium,  or  very  wet  mix- 
ture is  used.  A  rammer  for  dry  concrete  is 
~"N  shown  in  Fig.  1 ;  and  one  for  wet  concrete,  in 
Fig.  l.  Rammer  Fig.  2.  In  very  thin  walls,  where  a  wet  mix- 
tor 'Dry  Concrete  ture  ig  used>  often  the  tamping  or  puddling  is 

done  with  a  part  of  a  reinforcing  bar.  A  common  spade  is  fre- 
quently employed  for  the  face  of  work  to  push  back  stones 
that  may  have  separated  from  the  mass,  and  also  to  bring  the 
finer  portions  of  the  mass  to  the  face,  the  method  being  to  work 
the  spade  up  and  down  the  face  until  it  is  thoroughly  filled. 


REINFORCED  CONCRETE 


31 


Care  must  be  taken  not  to  pry  with  the  spade,  as  this  will  spring 
the  forms  unless  they  are  very  strong. 

Depositing  Concrete  under  Water.  In  depositing  concrete 
under  water,  some  means  must  be  taken  to  prevent  the  sep- 
aration of  the  materials  while  passing  through  the  water.  The 
three  principal  methods  are  as  follows: 

(1)  By  means  of  closed  buckets 

(2)  By  means  of  cloth  or  paper  bags 

(3)  By  means  of  tubes 

Buckets.  For  depositing  concrete  by  the  first  method,  special 
buckets  are  made  with  a  closed  top  and  hinged  bottom.  Con- 
crete deposited  under  water  must  be  disturbed 
as  little  as  possible,  and  tipping  a  bucket  is 
likely  to  disturb  it.  Several  different  types  of 
buckets  with  hinged  bottoms  have  been  devised 
to  open  automatically  when  they  reach  the 
place  for  depositing  the  concrete.  In  one  type, 
the  latches  which  fasten  the  trap-doors  are 
released  by  the  slackening  of  the  rope  when 
the  bucket  arrives  at  the  bottom,  and  the  doors 
are  open  as  soon  as  the  bucket  begins  to  ascend. 
In  another  type,  in  which  the  handle  extends 
down  the  sides  of  the  bucket  to  the  bottom,  the 
doors  are  opened  by  the  handles  sliding  down 


>n- 

I 


when  the  bucket  reaches  the  bottom.  The  doors  Fig.  2.  Rammer 
are  hinged  to  the  sides  of  the  bucket  and,  when  for  Wet  Coucrete 
opened,  permit  the  concrete  to  be  deposited  in  one  mass.  In 
depositing  concrete  by  this  means,'  it  is  found  rather  difficult 
to  place  the  layers  uniformly  and  to  prevent  the  formation  of 
mounds. 

Bags.  This  method  of  depositing  concrete  under  water  is 
by  means  of  open-woven  bags  or  paper  bags,  two-thirds  to 
three-quarters  full.  The  bags  are  sunk  in  the  water  and 
placed  in  courses,  if  possible  header  and  stretcher  system,  each 
course  being  arranged  as  laid.  The  texture  of  the  bagging  is 
close  enough  to  keep  the  cement  from  washing  out  and,  at  the 
same  time,  open  enough  to  allow  the  whole  to  unite  into  a 


32  REINFORCED  CONCRETE 

compact  mass.  The  fact  that  the  bags  are  crushed  into  irregu- 
lar shapes  which  fit  into  each  other  tends  to  lock  them  together 
in  a  way  that  makes  even  an  imperfect  joint  very  effective. 
When  the  concrete  is  deposited  in  paper  bags,  the  water  quickly 
soaks  the  paper ;  but  the  paper  retains  its  strength  long  enough 
for  the  concrete  to  be  deposited  properly. 

Tubes.  The  third  method  of  depositing  concrete  under 
water  is  by  means  of  long  tubes,  4  to  14  inches  in  diameter. 
The  tubes  extend  from  the  surface  of  the  water  to  the  place 
where  the  concrete  is  to  be  deposited.  If  the  tube  is  small— 
4  to  6  inches  in  diameter— a  cap  is  placed  over  the  bottom,  the 
tube  filled  with  concrete  and  lowered.  When  the  bottom  is 
reached  the  cap  is  withdrawn,  and  as  fast  as  the  concrete 
drops  out,  more  is  put  in  at  the  top  of  the  tube,  and  there  is 
thu's  a  continuous  stream  of  concrete  deposited. 

When  a  large  tube  is  used  to  deposit  concrete  in  this  manner, 
it  will  be  too  heavy  to  handle  conveniently  if  filled  before  being 
lowered,  and  the  empty  tube  is  consequently  lowered  until  the 
foot  of  the  tube  reaches  the  bottom.  The  water  rises  into  the 
chute  to  the  same  level  as  that  outside,  and  into  this  water  the 
concrete  must  be  dumped  until  the  water  is  wholly  replaced  or 
absorbed  by  the  concrete.  This  has  a  tendency  to  separate  the 
cement  from  the  sand  and  gravel,  and  it  will  take  a  yard  or 
more  of  concrete  to  displace  the  water  in  the  chute.  There  is  a 
danger  that  this  amount  of  badly  washed  concrete  will  be 
deposited  whenever  it  is  necessary  to  charge  the  chute,  a  danger 
which  occurs  not  only  when  the  charge  is  accidentally  lost,  but 
whenever  the  work  is  begun,  in  the  morning  or  at  any  other 
time.  Each  time  the  work  is  stopped,  the  charge  must  be 
allowed  to  run  out,  or  it  would  set  in  the  tube.  The  tubes  are 
usually  charged  by  means  of  wheelbarrows,  and  a  continuous 
flow  of  concrete  must  be  maintained.  When  the  chute  has 
been  filled,  it  is  raised  slowly  from  the  bottom,  and  a  part  of 
the  concrete  allowed  to  run  out  in  a  conical  heap  at  the  foot. 

This  method  has  also  been  employed  for  grouting  stone,  a 
2-inch  pipe,  perforated  at  the  bottom,  being  used.  The  grout, 
on  account  of  its  great  specific  gravity,  is  sufficient  to  replace 


REINFORCED  CONCRETE  33 

the  water  in  the  spaces  between  the  stones,  and  firmly  to  cement 
the  stones  into  a  mass  of  concrete.  A  mixture  of  one  part 
cement  and  one  part  sand  is  the  leanest  mixture  that  can  be 
used  for  this  purpose,  as  there  is  a  great  tendency  for  the 
cement  and  sand  to  separate. 

Bonding  Old  and  New  Concrete.  To  secure  a  water-tight 
joint  between  old  and  new  concrete  requires  a  great  deal  of 
care.  Where  the  strain  is  chiefly  compressive,  as  in  founda- 
tions, the  surface  of  concrete  laid  on  the  previous  day  should 
be  washed  with  clean  water,  no  other  precautions  being  neces- 
sary. In  walls  and  floors,  or  where  a  tensile  stress  is  likely  to 
be  applied,  the  joint  should  be  thoroughly  washed  and  soaked, 
and  then  painted  with  neat  cement  or  a  mixture  of  one  part 
cement  and  one  part  sand,  made  into  a  very  thin  mortar. 

In  the  construction  of  tanks  or  any  other  work  that  is  to  be 
water-tight,  in  which  the  concrete  is  not  placed  in  one  con- 
tinuous operation,  one  or  more  square  or  V-shaped  joints  are 
necessary.  These  joints  are  formed  by  a  piece  of  timber,  say 
4  inches  by  6  inches,  imbedded  in  the  surface  of  the  last  con- 
crete laid  each  day.  On  the  following  morning,  when  the 
timber  is  removed,  the  joint  is  washed  and  coated  with  neat 
cement  or  1 : 1  mortar.  The  joints  may  be  either  horizontal 
or  vertical.  The  bond  between  old  and  new  concrete  may  be 
aided  by  roughening  the  surface,  after  ramming  or  before 
placing  the  new  concrete. 

Effects  of  Freezing  of  Concrete.  Many  experiments  have 
been  made  to  determine  the  effect  of  freezing  of  concrete  before 
it  has  a  chance  to  set.  Both  from  these  experiments  and  from 
practical  experience,  it  is  now  generally  accepted  that  the  ulti- 
mate effect  of  freezing  of  Portland  cement  concrete  is  to 
produce  only  a  surface  injury.  The  setting  and  hardening  of 
the  concrete  is  retarded,  and  the  strength  for  short  periods  is 
lowered ;  but  the  ultimate  strength  appears  to  be  only  slightly, 
if  at  all,  affected.  A  thin  layer  about  &  inch  in  depth  is 
likely  to  scale  off  from  granolithic  or  concrete  pavements  which 
have  been  frozen,  leaving  a  rough  instead  of  a  troweled  wear- 
ing surface,  and  the  effect  upon  concrete  walls  is  often  similar ; 


34  REINFORCED  CONCRETE 

but  there  appears  to  be  no  other  injury.  Concrete  should  not 
be  laid  in  freezing  weather  if  that  can  be  avoided,  as  this 
involves  additional  expense  and  requires  greater  precautions; 
but  with  proper  care,  Portland  cement  concrete  can  be  laid  at 
almost  any  temperature. 

Preventive  Methods.  There  are  three  methods  which  may  be 
used  to  prevent  injury  to  concrete  laid  in  freezing  weather: 

(1)  Heat  the  sand  and  stone,  or  use  hot  water  in  mixing 

(2)  Add  salt,  calcium  chloride,  or  other 'chemicals,  to  lower  the  freez- 
ing point  of  the  water 

(3)  Protect  the  green  concrete  by  enclosing  it  and  keeping  the  tem- 
perature of  the  enclosure  above  the  freezing  point 

The  first  method  is  perhaps  more  generally  used  than  either 
of  the  others.  In  heating  the  aggregate,  the  frost  is  driven 
from  it;  hot  water  alone  is  insufficient  to  get  the  frost  out  of 
the  frozen  lumps  of  sand.  If  the  heated  aggregate  is  mixed 
with  water  which  is  hot  but  not  boiling,  experience  has  shown 
that  a  comparatively  high  temperature  can  be  maintained  for 
several  hours,  which  will  usually  carry  the  concrete  through 
the  initial  set  safely.  The  heating  of  the  materials  also  hastens 
the  setting  of  the  cement.  If  the  fresh  concrete  is  covered 
with  canvas  or  other  material,  that  will  assist  in  maintaining  a 
higher  temperature.  The  canvas,  however,  must  not  be  laid 
directly  on  the  concrete,  but  an  air  space  of  several  inches  must 
be  left  between  the  concrete  and  the  canvas. 

The  aggregate  is  heated  by  means  of  steam  pipes  laid  in  the 
bottom  of  the  bins,  or  by  having  pipes  of  strong  sheet  iron, 
about  18  inches  in  diameter,  laid  through  the  bottom  of  the  bins, 
and  fires  built  in  the  pipes.  The  water  may  be  heated  by 
steam  jets  or  other  means.  It  is  also  well  to  keep  the  mixer 
warm  in  severe  weather,  by  the  use  of  a  steam  coil  on  tlie 
outside,  and  jets  of  steam  on  the  inside. 

The  second  method— lowering  the  freezing  point  of  the 
water  by  adding  salt— has  been  commonly  used.  Salt  will 
increase  the  time  of  setting  and  lower  the  strength  of  the 
concrete  for  short  periods.  There  is  a  wide  difference  of 
opinion  as  to  the  amount  of  salt  that  may  be  used  without 


REINFORCED  CONCRETE  35 

lowering  the  ultimate  strength  of  the  concrete.  Specifications 
for  the  New  York  Subway  work  required  9  pounds  of  salt 
to  each  100  pounds  (12  gallons)  of  water  in  freezing  weather. 
A  common  rule  calls  for  10  per  cent  of  salt  to  the  weight  of 
water,  which  is  equivalent  to  about  13  pounds  of  salt  to  a 
barrel  of  cement. 

The  third  method  is  the  most  expensive,  and  is  used  only  in 
building  construction.  It  consists  in  constructing  a  light  wood 
frame  over  the  site  of  the  work,  and  covering  the  frame  with 
canvas  or  other  material.  The  temperature  of  the  enclosure  is 
maintained  above  the  freezing  point  by  means  of  stoves. 

WATERPROOFING   CONCRETE 

Concrete  Not  Generally  Water-Tight.  Concrete  as  ordina- 
rily mixed  and  placed  is  not  water-tight,  but  experience  has 
shown  that  where  concrete  is  proportioned  to  obtain  the  great- 
est density  practicable  and  is  mixed  wet,  the  resulting  concrete 
is  impervious  under  a  moderate  pressure.  The  concrete  of  the 
wet  mixtures  now  generally  used  in  engineering  work  possesses 
far  greater  density,  and  is  correspondingly  less  porous,  than 
the  dryer  mixtures  formerly  used.  However,  it  is  difficult,  on 
large  masses  of  work,  to  produce  concrete  of  such  close  texture 
as  to  prevent  seepage  at  all  points.  It  has  frequently  been 
observed  that  when  concrete  is  green  there  is  a  considerable 
seepage  through  it,  but  that  in  a  short  time  all  seepage  stops. 
Concrete  has  .been  made  practically  water-tight  by  forcing 
through  it  water  containing  a  small  amount  of  cement,  or 
cement  and  fine  sand. 

Effect  of  Steel  Reinforcement.  Reinforcing  steel  properly 
proportioned  and  located  both  horizontally  and  vertically  in 
long  walls,  subways,  and  reservoirs,  will  greatly  assist  in  ren- 
dering the  concrete  impervious  by  reducing  the  cracks  so  that 
if  they  do  occur  they  will  be  too  minute  to  permit  leakage,  or 
will  soon  fill  up  with  silt. 

Waterproofing  Methods.  Compounds  of  various  kinds  have 
been  mixed  with  concrete,  or  applied  as  a  wash  to  the  surface 
to  make  the  concrete  water-tight.  Many  of  the  compounds  are 


3G  REINFORCED  CONCRETE 

of  but  temporary  value,  and  in  time  lose  their  usefulness  as  a 
waterproofing  material. 

General  Considerations.  Several  successful  methods  of 
waterproofing  concrete  will  be  given  here,  most  of  which  will 
also  apply  to  stone  and  brickwork.  In  the  operation  of  water- 
proofing, a  very  common  mistake  is  made  by  applying  the 
waterproofing  materials  on  the  wrong  side  of  the  wall  to  be 
made  water-tight.  That  is,  if  water  finds  its  way  through  a 
cellar  wall,  it  is  useless  to  apply  a  waterproofing  coat  on  the 
inside  surface  of  the  wall,  as  the  pressure  of  the  water  will 
push  it  off.  (If  there  is  no  great  pressure  behind  it,  a  water- 
proofing coat  applied  on  the  inside  of  a  cellar  wall  may  be  suc- 
cessful in  keeping  moisture  out.)  To  be  successful  in  water- 
proofing a  cellar  wall,  however,  the  waterproofing  material 
should  be  applied  on  the  outside  surface  of  the  wall;  if  prop- 
erly applied,  the  wall,  as  well  as  the  cellar,  will  be  entirely 
free  of  water. 

In  tank  or  reservoir  construction,  the  conditions  are  different, 
in  that  it  is  generally  desired  to  prevent  the  escape  of  water. 
In  these  cases,  therefore,  the  waterproofing  is  applied  on  the 
inside  surface,  and  is  supported  by  the  materials  used  in  con- 
structing the  tank  or  reservoir.  The  structure  should  always 
be  designed  so  that  it  can  be  properly  waterproofed,  and  the 
waterproofing  should  always  be  applied  on  the  side  of  the  wall 
on  which  the  pressure  exists. 

Plastering.  For  cisterns,  swimming  pools,  or  reservoirs,  two 
coats  of  Portland  cement  grout — 1  part  cement,  2  parts  sand 
—applied  on  the  inside,  have  been  used  to  make  the  concrete 
water-tight.  One  inch  of  rich  mortar  has  usually  been  found 
effective  under  medium  pressure. 

At  Attleboro,  Massachusetts,  a  large  reinforced  concrete 
standpipe,  50  feet  in  diameter,  106  feet  high  from  the  inside 
of  the  bottom  to  the  top  of  the  cornice,  and  with  a  capacity  of 
1,500,000  gallons,  has  been  constructed,  and  is  in  the  service 
of  the  waterworks  of  that  city.  The  walls  of  the  standpipe 
are  18  inches  thick  at  the  bottom,  and  8  inches  thick  at  the  top. 
A  mixture  of  1  part  cement,  2  parts  sand,  and  4  parts  broken 


REINFORCED  CONCRETE  37 

stone,  the  stone  varying  from  |  inch  to  1^  inches,  was  used. 
The  forms  were  constructed,  and  the  concrete  placed,  in  sec- 
tions of  7  feet.  When  the  walls  of  the  tank  had  been  com- 
pleted, there  was  some  leakage  at  the  bottom  with  a  head  of 
water  of  100  feet.  The  inside  walls  were  then  thoroughly 
cleaned  and  picked,  and  four  coats  of  plaster  applied.  The 
first  coat  contained  2  per  cent  of  lime  to  1  part  of  cement  and 
1  part  of  sand;  the  remaining  three  coats  were  composed  of  1 
part  sand  to  1  part  cement.  Each  coat  was  floated  until  a 
hard  dense  surface  was  produced;  then  it  was  scratched  to 
receive  the  succeeding  coat. 

On  filling  the  standpipe  after  the  four  coats  of  plaster  had 
been  applied,  the  standpipe  was  found  to  be  not  absolutely 
water-tight.  The  water  was  drawn  out ;  and  four  coats  of  a 
solution  of  Castile  soap  and  four  of  alum  were  applied  alter- 
nately; and,  under  a  100-foot  head,  only  a  few  leaks  then 
appeared.  Practically  no  leakage  occurred  at  the  joints;  but 
in  several  instances  a  mixture  somewhat  wetter  than  usual  was 
used,  with  the  result  that  the  spading  and  ramming  served  to 
drive  the  stone  to  the  bottom  of  the  batch  being  placed,  and, 
as  a  consequence,  in  these  places  porous  spots  occurred.  The 
joints  were  obtained  by  inserting  beveled  tonguing  pieces,  and 
by  thoroughly  washing  the  joint  and  covering  it  with  a  layer 
of  thin  grout  before  placing  additional  concrete. 

Alum  and  Soap.  Mortar  may  be  made  practically  non- 
absorbent  by  the  addition  of  alum  and  potash  soap.  One  per 
cent  by  weight  of  powdered  alum  is  added  to  the  dry  cement 
and  sand,  and  thoroughly  mixed;  and  about  one  per  cent  of 
any  potash  soap  (ordinary  soft  soap)  is  dissolved  in  the  water 
used  in  the  mortar.  A  solution  consisting  of  1  pound  of 
concentrated  lye,  5  pounds  of  alum,  and  2  gallons  of  water, 
applied  while  the  concrete  is'  green  and  until  it  lathers  freely, 
has  been  successfully  used. 

Linseed  Oil.  Coating  the  surface  with  boiled  linseed  oil 
until  the  oil  ceases  to  be  absorbed  is  another  method  that  has 
been  tried  with  satisfaction. 

Hydrated  Lime.     Hydrated  lime  has  been  used  to  render 


38  REINFORCED  CONCRETE 

concrete  impervious,  with  favorable  results.  The  very  line 
particles  of  the  lime  fill  voids  that  would  otherwise  be  left, 
thereby  increasing  the  density  of  the  concrete.  For  a  1:2:4 
concrete  the  proper  amount  of  hydrated  lime  would  be  from 
6  to  8  per  cent  of  the  weight  of  the  cement  used.  When  the 
concrete  is  a  leaner  mixture  the  percentage  of  lime  is  increased ; 
that  is,  for  a  1 :  3 :  6  concrete  the  quantity  of  linie  is  sometimes 
as  much  as  16  or  18  per  cent. 

Sylvester  Process.  The  alternate  application  of  washes  of 
Castile  soap  and  alum,  each  being  dissolved  in  water,  is  known 
as  the  Sylvester  process  of  waterproofing.  Castile  soap  is  dis- 
solved in  water,  f  of  a  pound  of  soap  to  a  gallon  of  water, 
and  with  a  flat  brush  is  applied  boiling  hot  to  the  concrete 
surface,  care  being  taken  not  to  form  a  froth.  The  alum  dis- 
solved in  water— 1  pound  pure  alum  in  8  gallons  of  water— is 
applied  24  hours  later,  the  soap  having  had  time  to  become  dry 
and  hard.  The  second  wash  is  applied  in  the  same  manner  as 
the  first,  at  a  temperature  of  60  to  70  degrees  Fahrenheit.  The 
alternate  coats  of  soap  and  alum  are  repeated  every  24  hours. 
Usually  four  coats  will  make  an  impervious'  coating.  The 
soap  and  alum  combine  and  form  an  insoluble  compound,  fill- 
ing the  pores  of  the  concrete  and  preventing  the  seepage  of 
water.  The  walls  should  be  clean  and  dry,  when  the  composi- 
tion is  applied,  and  the  temperature  of  the  air  not  lower  than 
50  degrees  Fahrenheit.  The  concrete  should  be  still  green. 
This  method  of  waterproofing  has  been  used  extensively  for 
years,  and  has  generally  given  satisfactory  results  for  mod- 
erate pressures. 

Asphalt.  Asphalt  as  a  waterproofing  course  is  laid  in  thick- 
nesses from  £  to  1  inch,  usually  in  one  or  more  continuous 
sheets.  It  is  also  used  for  filling  in  contraction  joints  in  con- 
crete. The  backs  of  retaining  wills,  of  either  concrete,  stone, 
or  brick,  are  often  coated  with  asphalt  to  make  them  water- 
proof, the  asphalt  being  applied  hot  with  a  mop.  The  bottoms 
of  reservoirs  have  been  constructed  of  concrete  blocks  6  to 
8  feet  square  with  asphalt  joints  f  inch  to  £  inch  in  thickness 
and  extending  at  least  halfway  through  the  joint;  that  is,  for  a 


REINFORCED  CONCRETE 


39 


block  6  inches  in  thickness  the  asphalt  would'  extend  down  at 
least  3  inches. 

In  the  construction  of  the  filter  plant  at  Lancaster,  Penn- 
sylvania, in  1905,  a  pure-water  basin  and  several  circular  tanks 
were  constructed  of  reinforced  concrete.  The  pure-water 
basin  is  100  feet  wide  by  200  feet  long-  and  14  feet  deep,  with 
buttresses  spaced  12  feet  6  inches  center  to  center.  The  walls 
at  the  bottom  are  15  inches  thick,  and  12  inches  thick  at  the 
top.  Four  circular  tanks  are  50  feet  in  diameter  and  10  feet 
high,  and  eight  tanks  are  10  feet  in  diameter  and  10  feet  high. 
The  walls  are  10  inches  thick  at  the  bottom,  and  6  inches  at  the 
top.  The  concrete  was  a  wet  mixture  of  1  part  cement,  3  parts 
sand,  and  5  parts  stone.  No  waterproofing  material  was  used 
in  the  construction  of  the  tanks;  and  when  tested,  two  of  the 
50-foot  tanks  were 
found  to  be  water-tight, 
and  the  other  two  had 
a  few  leaks  where  wires 
which  had  been  used  to 
hold  the  forms  together 
had  pulled  out  when  the 
forms  were  taken  down. 
These  holes  were  stopped 
up  and  no  further  trouble  was  experienced.  In  constructing 
the  floor  of  the  pure-water  basin,  a  thin  layer  of  asphalt  was 
used,  as  shown  in  Fig.  3,  but  no  waterproofing  material  was 
used  in  the  walls,  and  both  were  found  to  be  water-tight. 

Felt  Laid  with  Asphalt  or  Coal  Tar.  Alternate  layers  of 
paper  or  felt  laid  with  asphalt  or  tar  are  frequently  used  to 
waterproof  floors,  tunnels,  subways,  roofs,  arches,  etc.  These 
materials  range  from  ordinary  tar  paper  laid  with  coal-tar 
pitch  or  asphalt  to  asbestos  or  asphalt  felt  laid  in  coal  tar  or 
asphalt.  Coal-tar  products  have  come  into  very  common  use 
for  this  work,  but  the  coal  tar  is  not  satisfactory  unless  it 
contains  a  large  percentage  of  carbon. 

In  using  these  materials  for  rendering  concrete  water-tight, 
usually  a  layer  of  concrete  or  brick  is  first  laid.  On  this  is 


Waterproofing^ 


Fig.  3.   Floor  of  Pure-Water  Basin 


40 


REINFORCED  CONCRETE 


mopped  a  layer  of  hot  asphalt;  felt  or  paper  is  then  laid  on 
the  asphalt,  the  paper  being-  lapped  from  6  to  12  inches. 
After  the  first  layer  of  felt  is  placed,  it  is  mopped  over  with 
hot  asphalt  compound,  and  another  layer  of  felt  or  paper  is 
laid,  the  operation  being  repeated  until  the  desired  thickness 
is  secured,  which  is  usually  from  2  to  10  layers— or,  in  other 
words,  the  waterproofing  varies  from  2-ply  to  10-ply.  A 
waterproofing  course  of  this  kind,  or  a  course  such  as  was 
described  in  the  paragraph  on  asphalt  waterproofing,  forms  a 
distinct  joint,  and  the  strength  in  bending  of  the  concrete  on 
the  two  sides  of  the  layer  must  be  considered  independently. 
When  asphalt,  or  asphalt  laid  with  felt  paper,  is  used  for 
waterproofing  the  interiors  of  the  walls  of  tanks,  a  4-inch 
course  of  brick  is  required  to  protect  and  hold  in  place  the 
waterproofing  materials.  Fig.  4*  shows  a  wall  section  of  a 
reservoir  constructed  for  the  New  York,  New  Haven  and 

Hartford  Railroad, 
which  illustrates  the 
methods  described 
above.  The  waterproof- 
ing material  for  the  res- 
ervoir consisted  of  4-ply 
Hydrex  felt,  and  Hy-' 
drex  compound  was  used 
to  cement  the  layers  to- 
gether. 

Fig.  5  is  an  illustra- 
tion of  the  method  used 
by  the  Barrett  Manu- 
facturing Company  in  applying  their  5-ply  coal-tar  pitch  and 
felt  roofing  material.  It  illustrates  in  a  general  way  the  method 
used  in  applying  waterproofing.  The  surfaces  to  be  water- 
proofed are  mopped  with  pitch  or  asphalt.  While  the  pitch  is 
still  hot,  a  layer  of  felt  is  placed,  which  is  followed  by  a  layer 
of  pitch  or  asphalt,  the  alternate  layers  succeeding  each  other 
until  the  required  number  of  layers  of  felt  has  been  secured. 
*  From  Engineering  Record,  September  21,  1907. 


}*•*•••*•'.*'•  '*.*• 


Fig.  4.    Method  of  Waterproofing  Reser- 
voirs by  Means  of  Hydrex  Felt 


REINFORCED  CONCRETE 


41 


In  no  place  should  one  layer  of  felt  be  permitted  to  touch  the 
layer  above  or  below  it.  When  the  last  layer  of  felt  is  laid  and 
thoroughly  mopped  with  the  coal  tar,  something  should  be 
placed  over  the  entire  surface  waterproofed  to  protect  it  from 
injury.  For  roofing,  this  protection  is  gravel,  Fig.  5. 


Fig.  5.    Section  Showing  Method  of  Waterproofing  Concrete 
Courtesy  of  Barrett  Manufacturing  Company 

In  waterproofing  the  back  of  concrete  or  stone  arches  usually 
a  layer  of  brick  is  placed  and  then  the  joints  between  the 
bricks  are  filled  with  pitch.  Brick  used  in  this  manner  also 
assist  in  holding  the  waterproofing  in  place.  Five  layers  of 
felt  and  pitch  should  be  a  sufficient  protection  against  a  head 
of  water  of  ten  feet. 

PRESERVATION  OF  STEEL  IN  CONCRETE 

Short-Time  Tests.  Tests  have  been  made  to  find  the  value 
of  Portland  cement  concrete  as  a  protection  for  steel  or  iron 
against  corrosion.  Nearly  all  of  the  tests  have  been, of  short 


42  REINFORCED  CONCRETE 

duration  (from  a  few  weeks  to  several  months)  ;  but  they  have 
clearly  shown  that  the  steel  or  iron  which  has  been  properly 
imbedded  in  concrete,  will  be  found  clean  and  bright,  when 
removed  therefrom.  Steel  removed  from  concrete  containing 
cracks  or  voids  usually  has  rust  at  the  points  where  the  voids 
or  cracks  occur;  but  if  the  steel  has  been  completely  covered 
with  concrete,  there  is  no  corrosion.  Tests  have  also  shown 
that  if  corroded  steel  is  imbedded  in  concrete,  the  concrete  will 
remove  the  rust.  To  secure  the  best  results,  the  concrete 
should  be  mixed  quite  wet,  and  care  should  be  taken  to  have 
the  steel  thoroughly  incased  in  the  concrete. 

Cinder  vs.  Stone  Concrete.  A  compact  cinder  concrete  has 
proved  about  as  effective  a  protection  for  steel  as  stone  con- 
crete. The  corrosion  found  in  cinder  concrete  is  mainly  due 
to  iron  oxide  or  rust  in  the  cinders,  and  not  to  the  sulphur. 
The  amount  of  sulphur  in  cinders  is  extremely  small,  and  there 
seems  to  be  little  danger  from  that  source.  A  steel-frame 
building  erected  in  New  York  in  1898  had  all  its  framework, 
except  the  columns,  imbedded  in  cinder  concrete;  when  the 
building  was  demolished  in  1903,  the  frame  showed  practically 
no  rust  which  could  be  considered  as  having  developed  after 
the  material  was  imbedded. 

Illustrations.  Cement  washes,  paints,  and  plasters  have 
been  used  for  a  long  time,  in  both  the  United  States  and 
Europe,  for  the  purpose  of  protecting  iron  and  steel  from  rust. 
The  engineers  of  the  Boston  Subway,  after  making  careful 
tests  and  investigations,  adopted  Portland  cement  paint  for  the 
protection  of  the  steel  work  in  that  structure.  The  railroad 
companies  of  France  use  cement  paint  extensively  to  protect 
their  metal  bridges  from  corrosion.  Two  coats  of  the  cement 
paint  and  sand  are  applie^l  with  leather  brushes. 

A  concrete-steel  water  main  on  the  Monier  system,  at 
Grenoble,  F'rance,  which  was  12  indies  in  diameter,  1.6  inches 
thick,  and  contained  a  steel  framework  of  |-inch  and  -^-inch 
steel  rods,  was  taken  up  after  15  years'  use  in  wet  ground. 
The  adhesion  was  found  perfect,  and  the  metal  absolutely  free 
from  rust. 


REINFORCED  CONCRETE  43 

William  Sooy  Smith,  M.  Am.  Soc.  C.  E.,  states  that  a  bed 
of  concrete  at  a  lighthouse  in  the  Straits  of  Mackinac,  10  feet 
below  water  surface,  was  removed  twenty  years  after  it  was 
laid,  and  the  imbedded  iron  drift-bolts  were  free  from  rust. 

An  excellent  example  of  the  preservation  of  steel  imbedded 
in  concrete  is  given  by  Mr.  H.  C.  Turner.*  Mr.  Turner's  com- 
pany had  recently  torn  down  a  section  of  a  one-story  reinforced 
concrete  building  erected  by  his  company  in  1902,  at  New 
Brighton,  Staten  Island.  The  building  had  a  pile  foundation, 
the  piles  being  cut  off.  at  mean  tide  level.  The  footings,  side 
walls,  columns,  and  roof  had  all  been  constructed  of  reinforced 
concrete.  In  concluding  his  account,  Mr.  Turner  says : 

All  steel  reinforcement  was  found  in  perfect  preservation,  excepting 
in  a  few  cases  where  the  hoops  were  allowed  to  come  closer  than  |  inch 
to  the  surface.  Some  evidence  of  corrosion  was  found  in  such  cases,  thus 
demonstrating  the  necessity  of  keeping  the  steel  reinforcement  at  least 
|  inch  from  the  surface.  The  footings  were  covered  by  the  tide  twice 
daily.  The  concrete  was  extremely  hard,  and  showed  no  weakness  what- 
ever from  the  action  of  the  salt  water.  The  steel  bars  in  the  footings 
were  perfectly  preserved,  even  in  cases  where  the  concrete  protection 
was  only  f  inch  thick. 

FIRE    PROTECTIVE  QUALITIES   OF    CONCRETE 

High  Resisting  Qualities.  The  various  tests  which  have 
been  conducted— including  the  involuntary  tests  made  as  the 
result  of  fires— have  shown  that  the  fire-resisting  qualities  of 
concrete,  and  even  its  resistance  to  a  combination  of  fire  and 
water,  are  greater  than  those  of  any  other  known  type  of 
building  construction.  Fires  and  experiments  which  test  build- 
ings of  reinforced  concrete  have  proved  that  where  the  tem- 
perature ranges  from  1400  to  1900  degrees  Fahrenheit,  the  sur- 
face of  the  concrete  may  be  injured  to  a  depth  of  i  to  f  inch 
or  even  of  one  inch;  but  the  body  of  Ihe  concrete  is  not  affected, 
the  only  repairs  required,  if  any,  being  a  coat  of  plaster. 

Thickness  of  Concrete  Required.  Actual  fires  and  tests 
have  shown  that  2  inches  of  concrete  will  protect  an  I-beam 
with  good  assurance  of  safety.  Reinforced  concrete  beams  and 
girders  should  have  a  clear  thickness  of  1£  inches  of  concrete 

*  Engineering  News,  January  16,  1908. 


44  REINFORCED  CONCRETE 

outside  the  steel  on  the  sides  and  2  inches  on  the  bottom ;  slabs 
should  have  at  least  1  inch  below  the  slab  bars,  and  columns 
2  inches.  Structural  steel  columns  should  have  at  least  2  inches 
of  concrete  outside  of  the  farthest  projecting  edge. 

Theory.  The  theory  of  the  fireproofing  qualities  of  Port- 
land cement  concrete  given  by  Mr.  Spencer  B.  Newberry  is  that 
the  capacity  of  the  concrete  to  resist  fire  and  prevent  its  trans- 
ference to  steel  is  due  to  its  combined  water  and  porosity.  In 
hardening,  concrete  takes  up  12  to  18  per  cent  of  the  water 
contained  in  the  cement.  This  water  is  chemically  combined, 
and  not  given  off  at  the  boiling  point.  On  heating,  a  part  of 
the  water  is  given  off  at  500  degrees  Fahrenheit,  but  dehydra- 
tion does  not  take  place  until  900  degrees  Fahrenheit  is 
reached.  The  mass  is  kept  for  a  long  time  at  comparatively 
low  temperature  by  the  vaporization  of  water  absorbing  the 
heat.  A  steel  beam  imbedded  in  concrete  is  thus  cooled  by  the 
volatilization  of  water  in  the  surrounding  concrete. 

Resistance  to  the  passage  of  heat  is  offered  by  the  porosity 
of  concrete.  Air  is  a  poor  conductor,  and  an  air  space  is  an 
efficient  protection  against  conduction.  The  outside  of  the  con- 
crete may  reach  a  high  temperature;  but  the  heat  only  slowly 
and  imperfectly  penetrates  the  mass,  and  reaches  the  steel  so 
gradually  that  it  is  given  off  as  fast  as  it  is  supplied. 

Cinder  vs.  Stone  Concrete.  Mr.  Newberry  says:  "Porous 
substances,  such  as  asbestos,  mineral  wool,  etc.,  are  always  used 
as  heat-insulating  material.  For  this  same  reason,  cinder  con- 
crete, being  highly  porous,  is  a  much  better  non-conductor  than 
a  dense  concrete  made  of  sand  and  gravel,  or  stone,  and  has  the 
added  advantage  of  being  light." 

Professor  Norton,  on  the  other  hand,  in  comparing  the 
actions  of  cinder  and  stone  concrete  in  the  great  Baltimore  fire 
of  February,  1904,*  states  that  there  is  but  little  difference  in 
the  two  concretes.  The  burning  of  bits  of  coal  in  poor  cinder 
concrete  is  often  balanced  by  the  splitting  of  stones  in  the 
stone  concrete.  "However,  owing  to  its  density,  the  stone  con- 
crete takes  longer  to  heat  through." 

*  Report  to  the  Insurance  Engineering  Experiment  Station. 


REINFORCED  CONCRETE  45 

Results  Shown  in  Baltimore  Fire.  Engineers  and  archi- 
tects, who  made  reports  on  the  Baltimore  fire,  generally  agree 
that  reinforced  concrete  construction  stood  very  well— much 
better  than  terra  cotta.  Professor  Norton  says: 

Where  concrete  floor-arches  and  concrete-steel  construction  received 
the  full  force  of  the  fire,  it  appears  to  have  stood  well,  distinctly  better 
than  the  terra  cotta.  The  reasons,  I  believe,  are  these  :  The  concrete 
and  steel  expand  at  sensibly  the  same  rate,  and  hence,  when  heated,  do 
not  subject  each  other  to  stress  ;  but  terra  cotta  usually  expands  about 
twice  as  fast  with  increase  in  temperature  as  steel,  and  hence  the  parti- 
tions and  floor-arches  soon  become  too  large  to  be  contained  by  the  steel 
members  which  under  ordinary  temperature  properly  enclose  them. 

STEEL  FOR   REINFORCING   CONCRETE 

Quality  of  Reinforcing  Steel.  Steel  for  reinforcing  con- 
crete is  not  usually  subjected  to  such  severe  treatment  as  ordi- 
nary structural  steel,  as  the  impact  effect  is  likely  to  be  a  little 
less;  but  the  quality  of  the  steel  should  be  carefully  specified. 
To  reduce  the  cost  of  reinforced  concrete  structures,  there  has 
been  a  tendency  to  use  cheap  steel,  and  this  has  resulted  in  bars 
being  rolled  from  old  railroad  rails.  These  bars  are  known  as 
rerolled  bars  and  they  should  always  be  thoroughly  tested  before 
being  used.  If  the  rails  from  which  the  bars  are.  rerolled  were 
of  good  material,  the  bars  should  prove  to  be  satisfactory,  but 
if  the  rails  contained  poor  materials  the  bars  rolled  from  them 
will  probably  be  brittle  and  easily  broken  by  a  sudden  blow. 
Many  engineers  specify  that  the  bars  shall  be  rolled  from 
billets  to  avoid  using  any  old  material. 

The  grades  of  steel  used  in  reinforced  concrete  range  from 
soft  to  hard,  and  may  be  classified  under  three  heads:  soft, 
medium,  and  hard. 

Soft  Steel.  Soft  steel  has  an  ultimate  strength  of  50,000  to 
58,000  pounds  per  square  inch.  It  is  seldom  used  in  reinforced 
concrete. 

Medium  Steel.  Medium  steel  has  an  ultimate  strength  of 
55,000  to  65,000  pounds  per  square  inch.  The  elastic  limit  is 
from  32,000  to  38,000  pounds  per  square  inch.  This  grade  of 
steel  is  extensively  used  for  reinforced  concrete  work  and  can 
be  bought  in  the  open  market  and  used  with  safety. 


46  REINFORCED  CONCRETE 

Hard  Steel.  Hard  steel,  better  known  as  high-carbon  steel, 
should  have  an  ultimate  strength  of  85,000  to  100,000  pounds 
per  square  inch ;  and  the  elastic  limit  should  be  from  50,000  to 
65,000  pounds  per  square  inch.  The  hard  steel  has  a  greater 
percentage  of  carbon  than  the  medium  steel,  and  therefore  the 
yield  point  is  higher.  This  steel  is  preferred  by  some  engineers 
for  reinforced  concrete  work,  but  it  should  be  thoroughly  tested 
to  be  sure  that  it  is  according  to  specifications.  This  is  the 
grade  of  steel  into  which  old  rails  are  rolled,  but  it  is  also 
rolled  from  billets. 

Processes  of  Making  Steel.  Reinforcing  bars  are  rolled  by 
both  the  Bessemer  and  the  open-hearth  processes.  Bars  rolled 
by  either  process  make  good  reliable  steel,  but  bars  rolled  by 
open-hearth  process  are  generally  more  uniform  in  quality. 

Types  of  Bars 

The  steel  bars  used  in  reinforcing  concrete  usually  consist  of 
small  bars  of  such  shape  and  size  that  they  may  be  easily  bent 
and  placed  in  the  concrete  so  as  to  form  a  monolithic  structure. 
To  distribute  the  stress  in  the  concrete,  and  secure  the  necessary 
bond  between  the  steel  and  concrete,  the  steel  required  must  be 
supplied  in  comparatively  small  sections.  All  types  of  the 
regularly  rolled  small  bars  of  square,  round,  and  rectangular 
section,  as  well  as  some  of  the  smaller  sections  of  structural 
steel,  such  as  angles,  T-bars,  and  channels,  and  also  many  spe- 
cial rolled  bars,  have  been  used  for  reinforcing  concrete.  These 
bars  vary  in  size  from  £  inch  for  light  construction,  up  to  1£ 
inches  for  heavy  beams,  and  2  inches  for  large  columns.  In 
Europe  plain  round  bars  have  been  extensively  used  for  many 
years;  they  have  also  been  used  in  the  United  States,  but  not 
to  the  same  extent  as  in  Europe.  In  America  a  very  much 
larger  percentage  of  work  has  been  done  with  deformed  bars. 

Plain  Bars.  With  plain  bars,  the  transmission  of  stresses 
is  dependent  upon  the  adhesion  between  the  concrete  and  the 
steel.  Square  and  round  bars  show  about  the  same  adhesive 
strength,  but  the  adhesive  strength  of  the  flat  bars  is  far  below 
that  of  the  round  and  square  bars.  The  round  bars  are  more 


REINFORCED  CONCRETE  47 

convenient  to  handle  and  more  easily  obtained,  and  have,  there- 
fore, generally  been  used  when  plain  bars  were  desirable. 

Steel  Sections.  Small  angles,  T-bars,  and  channels  have 
been  used  to  a  greater  extent  in  Europe  than  in  this  country. 
They  are  principally  used  where  riveted  skeleton  work  is  pre- 
pared for  the  steel  reinforcement;  and  in  this  case  it  is  usually 
desirable  to  have  the  steel  work  self-supporting. 

Deformed  Bars.  There  are  many  forms  of  reinforcing  ma- 
terials on  the  market,  differing  from  one  another  in  the  manner 
of  forming  the  irregular  projections  on  their  surface.  The 
object  of  all  these  special  forms  of  bars  is  to  furnish  a  bond 


Fig.  6.    Square  Twisted  Reinforcing  Steel  Bar 
Courtesy  of  Inland  Steel  Company 

with  the  concrete,  independent  of  adhesion.  This  bond  formed 
between  the  deformed  bar  and  the  concrete  is  usually  called  a 
mechanical  bond.  Some  of  the  most  common  types  of  bars 
used  are  the  square  twisted  bar,  the  corrugated)  the  Havemeyer, 
and  the  Kahn. 

Square  Twisted  Bar.  The  twisted  bar,  shown  in  Fig.  6, 
was  one  of  the  first  steel  bars  shaped  to  give  a  mechanical  bond 
with  concrete.  This  type  of  bar  is  a  commercial  square  bar 
twisted  while  cold.  There  are  two  objects  in  twisting  the  bar— 
first,  to  give  the  metal  a  mechanical  bond  with  the  concrete ; 
second,  to  increase  the  elastic  limit  and  ultimate  strength  of 
the  bar.  In  twisting  the  bars,  usually  one  complete  turn  is 
given  the  bar  in  nine  or  ten  diameters  of  the  bar,  with  the 
result  that  the  elastic  limit  of  the  bar  is  increased  from  40  to 
50  per  cent,  and  the  ultimate  strength  is  increased  from  25  to 
35  per  cent.  These  bars  can  readily  be  bought  already  twisted ; 
or,  if  it  is  desired,  square  bars  may  be  bought  and  twisted  on 
the  site  of  the  work. 

Corrugated  Bar.  The  corrugated  bar,  which  has  corruga- 
tions as  shown  in  Fig.  7,  was  invented  by  Mr.  A.  L.  Johnson, 
M.  Am.  Soc.  C.  E.  These  corrugations,  or  square  shoulders, 


48 


REINFORCED  CONCRETE 


are  placed  at  right  angles  to  the  axis  of  the  bar,  and  their  sides 
make  an  angle  with  the  perpendicular  to  the  axis  of  the  bars 
not  exceeding  the  angle  of  friction  between  the  bar  and  con- 


Fig.  7.   Corrugated  Bar  for  Reinforcement  of  Concrete 
Courtesy  of  Corrugated  Bar  Company 

crete.  These  bars  are  usually  rolled  from  high-carbon  steel 
having  an  elastic  limit  of  55,000  to  65,000  pounds  per  square 
inch  and  an  ultimate  strength  of  about  100,000  pounds  per 
square  inch.  They  are  also  rolled  from  any  quality  of  steel 
desired.  In  size  they  range  from  |  inch  to  1£  inches,  their 


Fig.  8.  Havemeyer  Bar  for  Reinforcement  of  Concrete 
Courtesy  of  Concrete  Steel  Company 

sectional  area  being  the  same  as  that  of  plain  bars  of  the  same 
size.  These  bars  are  rolled  in  both  the  common  types,  round 
and  square. 

Havemeyer  Bar.  The  Havemeyer  bar,  Fig.  8,  was  invented 
by  Mr.  J.  F.  Havemeyer.  This  has  a  uniform  cross  section 
throughout  its  length.  The  bonding  of  the  bar  to  the  concrete 
is  uniform  at  all  points,  and  the  entire  section  is  available  for 
tensile  strength. 

Kahn  Bar.  The  Kahn  bar,  Fig.  9,  was  invented  by  Mr. 
Julius  Kahn,  Assoc.  M.  Am.  Soc.  C.  E.  This  bar  is  designed 


Fig.  9.    Kahn  Trussed  Bar  for  Reinforcement  of  Concrete 
Courtesy  of  The  Kahn  System 

with  the  assumption  that  the  shear  members  should  be  rigidly 
connected  to  the  horizontal  members.     The  bar  is  rolled  with 


REINFORCED  CONCRETE 


49 


TABLE  IX 
Standard  Sizes  of  Expanded  Metal 


MESH'  IN 

INCHES 

({AGE 
No. 

WEIGHT  IN  LB. 
PER  SQ.  FT. 

SECTIONAL  AREA 
1  FOOT  WIDE 
IN  SQ.  JN. 

3 

16 

.30 

.082 

8 

10 

.625 

.177 

6 

4 

.86 

.243 

a  cross  section  as  shown  in  the  figure.  The  thin  edges  are  cut 
and  turned  up,  and  form  the  shear  members.  These  bars  are 
manufactured  in  several  sizes. 

Expanded  Metal.  Expanded  metal,  Fig.  10,  is  made  from 
plain  sheets  of  steel,  slit  in  regular  lines  and  opened  into 
meshes  of  any  desired  size  or  section  of  strand.  It  is  commer- 


Fig.  10.    Example  of  Expanded  Metal  Fabric 
Courtesy  of  Nor  tine  eatern  Expanded  Metal  Company 

cially  designated  by  giving  the  gage  of  the  steel  and  the  amount 
of  displacement  between  the  junctions  of  the  meshes.  The 
most  common  manufactured  sizes  are  given  in  Table  IX. 

Steel  Wire  Fabric.  Steel  wire  fabric  reinforcement  con- 
sists of  a  netting  of  heavy  and  light  wires,  usually  with  rectan- 
gular meshes.  The  heavy  wires  carry  the  load,  and  the  light 
ones  are  used  to  space  the  heavier  ones.  There  are  many  forms 
of  wire  fabric  on  the  market. 

Table  X  is  condensed  from  the  handbook  of  the  Cambria 


50 


REINFORCED  CONCRETE 


TABLE  X 

Weights  and  Areas  of  Square  and  Round  Bar 

(One  cubic  foot  of  steel  weighs  489.6  pounds) 


THICKNESS 

OR 

DIAMETER 
(Inches) 

WEIGHT  OF 
SQUARE  BAR, 
1  FOOT  LONG 
(Pounds) 

WEIGHT  OF 
ROUND  BAR, 
1  FOOT  LONG 
(Pounds) 

AREA  OP 
SQUARE  BAR, 
(Sq.  In.) 

AREA  OP 
ROUND  BAR, 
(Sq.  In.) 

ClRCUM.  OP 

ROUND  BAR, 
(Inches) 

| 

.213 

.167 

.0625 

.0491 

.7854 

A 

.332 

.261 

.0977 

.0767 

.9817 

1 

.478 

.376 

.1406 

.1104 

1.1781 

.651 

.511 

.1914 

.1503 

1.3744 

P 

.850 

.668 

.2500 

.1963 

1.5708 

| 

1.328 

1.043 

.3906 

.3068 

1.9635 

i 

1.913 

1.502 

.5625 

.4418 

2.3562 

i 

3.400 

2.670 

1.0000 

.7854 

3.1416 

1J 

4.303 

3.379 

1.2656 

.9940 

3.5343 

if 

5.312 

4.173 

1.5625 

1.2272 

3.9270 

U 

7.650 

6.008 

2.2500 

1.7671 

4.7124 

if 

10.41 

8.178 

3.0625 

2.4053 

5.4978 

2 

13.60 

10.68 

4.0000 

3.1416 

6.2832 

Steel  Company,  and  gives  the  standard  weights  and  areas  of 
plain  round  and  square  bars  commonly  used  in  reinforced  con- 
crete construction . 

REINFORCED  CONCRETE  BEAM  DESIGN 
GENERAL  THEORY  OF  FLEXURE 

The  theory  of  flexure  in  reinforced  concrete  is  exceptionally 
complicated.  A  multitude  of  simple  rules,  formulas,  and 
tables  for  designing  reinforced-concrete  work  have  been  pro- 
posed, some  of  which  are  sufficiently  accurate  and  applicable 
under  certain  conditions.  But  the  effect  of  these  various  condi- 
tions should  be  thoroughly  understood.  Reinforced  concrete 
should  not  be  designed  by  "rule-of-thumb"  engineers.  It  is 
hardly  too  strong  a  statement,  to  say  that  a  man  is  criminally 
careless  and  negligent  when  he  attempts  to  design  a  structure 
on  which  the  safety  and  lives  of  people  will  depend,  without 
thoroughly  understanding  the  theory  on  which  any  formula  he 
may  use  is  based.  The  applicability  of  all  formulas  is  so  de- 
pendent on  the  quality  of  both  the  steel  and  the  concrete,  as 
well  as  on  many  of  the  details  of  the  design,  that  a  blind  appli- 
cation of  a  formula  is  very  unsafe.  Although  the  greatest 


REINFORCED  CONCRETE  51 

pains  will  be  taken  to  make  the  following  demonstration  as 
clear  and  plain  as  possible,  it  will  be  necessary  to  employ  sym- 
bols, and  to  work  out  several  algebraic  formulas  on  which  the 
rules  for  designing  will  be  based.  The  full  significance  of  many 
of  the  following  terms  may  not  be  fully  understood  until  sev- 
eral subsequent  paragraphs  have  been  studied. 

SYMBOLS  DEFINED 

6  =  Breadth  of  concrete  beam 

d  —  Depth  from  compression  face  to  center  of  gravity  of  the  steel 
A  =  Area  of  the  steel 

A 
p  =  -j-r   =  Ratio  of  area  of  steel  to  area  of  concrete  above  the 

center  of  gravity  of  the  steel,  generally  referred  to  as 

percentage  of  reinforcement 
Es  =  Modulus  of  elasticity  of  steel 
Ec  =  Initial  modulus  of  elasticity  of  concrete 

®8 

n  =  -77-  =  Ratio  of  the  moduli 

Lc 

s  =  Tensile  stress  per  unit  of  area  in  steel 
o=  Compressive  stress  per  unit  of  area  in  concrete  at  the  outer 

fiber  of  the  beam 

es  =  Deformation  per  unit  of  length  in  the  steel 
ec  <=  Deformation  per  unit  of  length  in  outer  fiber  of  concrete 
Jc  =  Ratio  of  dimension  from  neutral  axis  to  center  of  compressive 

stresses  to  the  total  effective  depth  d 
•    j=  Ratio    of    dimension    from    steel    to    center    of    compressive 

stresses  to  the  total  effective  depth  d 

(D  —  Distance    from    compressive    face   to    center    of    compressive 
*  stresses 

2  X  —  Summation  of  horizontal  compressive  stresses 
M  =  Resisting  moment  of  a  section 

Statics  of  Plain  Homogeneous  Beams.  As  a  preliminary 
tr  the  theory  of  the  use  of  reinforced  concrete  in  beams,  a  very 
brief  discussion  will  be  given  of  the  statics  of  an  ordinary 
homogeneous  beam,  made  of  a  material  whose  moduli  of  elas- 
ticity in  tension  and  compression  are  equal.  Let  A  B,  Fig.  11, 
represent  a  beam  carrying  a  uniformly  distributed  load  W; 
then  the  beam  is  subjected  to  transverse  stresses.  Let  us 
imagine  that  one-half  of  the  beam  is  a  "free  body"  in  space 
and  is  acted  on  by  exactly  the  same  external  forces;  let  us  also 
assume  forces  C  and  T  (acting  on  the  exposed  section),  which 
are  just  such  forces  as  are  required  to  keep  that  half  of  the 


52 


REINFORCED  CONCRETE 


beam  in  equilibrium.    These  forces  and  their  direction  are  rep- 
resented in  the  lower  diagram  by  arrows.    The  load  W  is  repre- 


I  H 


Fig.  11.   Diagram  of  Beam  Carr 
Distributed  Loa~ 


Uniformly 


sented  by  the  series  of  small,  equal,  and  equally  spaced  vertical 
arrows  pointing  downward.  The  reaction  of  the  abutment 
against  the  beam  is  an  upward  force,  shown  at  the  left.  The 
forces  acting  on  a  section. at  the  center  are  the  equivalent  of  the 
two  equal  forces  C  and  T. 

The  force  C,  acting  at  the  top  of  the  section,  must  act  toward 
the  left,  and  there  is  therefore  compression  in  that  part  of  the 
section.  Similarly,  the  force  T  is  a  force  acting  toward  the 
right,  and  the  fibers  of  the  lower  part  of  the  beam  are  in 
tension.  For  our  present  purpose  we  may  consider  that  the 
forces  C  and  T  are  in  each  case  the  resultant  of  the  forces 
acting  on  a  very  large  number  of  fibers.  The  stress  in  the  outer 
fibers  is,  of  course,  greatest.  At  the  center  of  the  height,  there 
is  neither  tension  nor  compression.  This  is  called  the  neutral 
axis,  Fig.  12. 

Let  us  consider,  for  the  sake 
of  simplicity,  a  very  narrow 
portion  of  the  beam,  having  the 
full  length  and  depth  but  so 
narrow  that  it  includes  only  one 
set  of  fibers,  one  above  the  other, 
as  shown  in  Fig.  13.  In  the  case 
of  a  plain  rectangular  homo- 
geneous beam,  the  elasticity 
being  assumed  equal  for  tension  and  compression,  the  stresses 
in  the  fibers  would  be  as  given  in  Fig.  12;  the  neutral  axis 


AXIS 


NEUTRAL 


Fig.  12.  Diagram  Showing  Posi- 
tion of  Neutral  Axis  in  Beam 


REINFORCED  CONCRETE 


53 


would  be  at  the  center  of  the  height,  and  the  stress  at  the  bottom 
and  the  top  would  be  equal  but  opposite.  If  the  section  were 
at  the  center  of  the  beam,  with  a  uniformly  distributed  load,  as 
indicated  in  Fig.  11,  the  shear  would  be  zero. 

A  beam  may  be  constructed  of  plain  concrete;  but  its 
strength  will  be  very  small,  since  the  tensile  strength  of  con- 
crete is  comparatively  insignificant.  Reinforced  concrete  util- 
izes the  great  tensile  strength  of  steel  in  combination  with  the 
compressive  strength  of  concrete.  It  should  be  realized  that 
two  of  the  most  essential  qualities  are  compression  and  tension, 
and,  other  things  being  equal,  the  cheapest  method  of  obtaining 
the  proper  compression  and  tension  is  the  most  economical. 
Statics  of  Reinforced  Concrete  Beams 

In  a  reinforced  concrete  beam,  the  steel  is  placed  in  the 
tension  side  of  the  beam.  Usually  it  is  placed  1  to  2  inches 
from  the  outer  face,  with  the  double  purpose  of  protecting 
the  steel  from  corrosion  or  fire,  and  of  making  more  certain 
the  union  of  the  concrete  and  the 
steel;  but  the  concrete  below  the 
steel  is  not  considered  in  the  numer- 
ical calculations.  The  concrete  be- 
tween the  steel  and  the  neutral  axis 
performs  the  very  necessary  func- 
tion of  transmitting  the  tension  in 
the  steel  to  the  concrete.  This  stress 
is  called  shear  and  is  discussed  later. 
Although  the  concrete  in  the  lower 
part  of  the  beam  is,  theoretically, 
subject  to  the  tension  of  transverse  stress  and  does  actually 
contribute  its  share  of  the  tension  when  the  stresses  in  the  beam 
are  small,  the  proportion  of  the  necessary  tension  which  the 
concrete  can  furnish  when  the  beam  is  heavily  loaded  is  so  very 
little  that  it  is  usually  ignored,  especially  since  such  a  policy  is 
on  the  side  of  safety,  and  also  since  it  greatly  simplifies  the 
theoretical  calculations  and  yet  makes  very  little  difference  in 
the  final  result.  We  may,  therefore,  consider  that  in  a  unit 
section  of  the  beam,  Fig.  14,  the  concrete  above  the  neutral  axis 


Fig.  13.    Diagram  Showing 

Position  of  Neutral  Axis 

in  Narrow  Beam 


54 


REINFORCED  CONCRETE 


is  subject  to  compression,  and  that  the  tension  is  furnished 
entirely  by  the  steel. 

Elasticity  of  Concrete  in  Compression.  In  computing  the 
transverse  stresses  in  a  wood  beam  or  steel  I-beam,  it  is  as- 
sumed that  the  modulus  of  elasticity  is  uniform  for  all  stresses 
within  the  elastic  limit.  Experimental  tests  have  shown  this  to  be 
so  nearly  true  that  it  is  accepted  as  a  mechanical  law.  This 
means  that  if  a  force  of  1,000  pounds  is  required  to  stretch  a 
bar  .001  of  an  inch,  it  will  require  2,000  pounds  to  stretch  it 
.002  of  an  inch.  Similar  tests  have  been  made  with  concrete, 
to  determine  the  law  of  its  elasticity,  but  unfortunately,  con- 
crete is  not  so  nearly  uniform  in 
its  behavior  as  steel  and  the  re- 
sults of  the  tests  are  somewhat 
erratic. 

It  was  formerly  rather  com- 
mon to  base  the  computation  of 
formulas  on  the  assumption  that 
the  curve  of  compression  for  con- 
crete is  a  parabola.  The  develop- 
ment of  the  theory  is  complex, 
but  it  has  been  found  that  for  a 
compression  of  600  or  even  800  pounds  per  square  inch,  the 
parabolic  curve  is  not  very  different  from  a  straight  line.  A 
comparison  of  the  results  based  on  the  strict  parabolic  theory 
with  those  based  on  the  simpler  straight-line  formulas  shows 
that  the  difference  is  small  and  often  not  greater  than  the 
uncertainty  as  to  the  true  strength  of  the  concrete.  The  straight- 
line  theory  will,  therefore,  be  used  exclusively. 

Theoretical  Assumptions.     The  theory  of  reinforced  con- 
crete beams  is  based  on  the  usual  assumptions  that : 

(1)  The  loads  are  applied  at  right  angles  to  the  axis  of  the  beam. 
The  usual  vertical  gravity  loads  supported  by  a  horiz:ntal  beam  fulfil 
this  condition. 

(2)  There  is  no  resistance  to  free  horizontal  motion.     This   condi- 
tion is  seldom,  if  ever,  exactly  fulfilled  in  practice.     The  more  rigidly 
the  beam  is  held  at  the  ends,  the  greater  will  be  its  strength  above 
that  computed  by  the   simple  theory.     UAder  ordinary  conditions  the 
added  strength  .is  quite  indeterminate  and  is  not  allowed  for. 


Fig.     14.      Diagram     Showing 

Transmission    of    Tension 

in    Steel   to    Concrete 


REINFORCED  CONCRETE 


55 


(3)  The   concrete   and   steel   stretch   together   without    breaking  the 
bond  between  them.     This  is  absolutely  essential. 

(4)  Any  section  of  the  beam  which  is  plane  before  bending  is  plane 
after  bending. 

In  Fig'.  15-is  shown,  in  a  very  exaggerated  form,  the  essential 
meaning  of  assumption  (4).  The  section  abdc  in  the  unstrained 
condition,  is  changed  to  the  plane  a'b'd'c'  when  the  load  is  ap- 
plied. The  compression  at  the  top  equals  aa'  equals  bb'.  The 
neutral  axis  is  unchanged.  The  concrete  at  the  bottom  is 
stretched  an  amount  equal  to  cc'  equals  dd'f  while  the  stretch  in 
the  steel  equals  gg'.  The  compression  in  the  concrete  between 

i 


TKfl'- 


Pig.  15.  Exaggerated  Diagram  Showing  Plane 
Section  of  Beam  before  and  after  Bending 

the  neutral  axis  and  the  top  is  proportional  to  the  distance  from 
the  neutral  axis. 

In  Fig.  16  is  given  a  side  view  of  the  beam,  with  special 
reference  to  the  deformation  of  the  fibers.  Since  the  fibers 
between  the  neutral  axis  and  the  compressive  face  are  com- 
pressed proportionally,  then,  if  aa'  represents  the  lineal  com- 
pression of  the  outer  fiber,  the  shaded  lines  represent,  at  the 
same  scale,  the  compression  of  the  intermediate  fibers. 

Summation  of  Compressive  Forces.  The  summation  of 
compressive  forces  evidently  equals  the  sum  of  all  the  com- 
pressions, varying  from  zero  to  the  maximum  compressive 
stress  c  at  the  extreme  upper  fiber,  where  the  lineal  compression 
is  ec.  The  average  unit,  compressive  stress  is,  therefore,  £  c. 


56 


REINFORCED  CONCRETE 


Since  k  is  the  ratio  of  the  distance  from  the  neutral  axis  to  the 
upper  fiber  to  the  total  effective  depth  d,  that  distance  equals  ltd. 
The  breadth  of  the  beam  is  b;  therefore 


.  (1) 

Center  of  Gravity  of  Compressive  Forces.  The  center  of 
gravity  of  compressive  forces  is  sometimes  called  the  centroid 
of  compression.  It  here  coincides  with  the  center  of  gravity  of 
the  triangle,  which  is  at  one-third  the  height  of  the  triangle 
from  the  upper  face.  Therefore 

x  =  $kd  (2) 

The  ratio  of  the  dimension  from  the 
steel  to  the  center  of  the  compressive 
stress  to  the  dimension  d  equals  j  and, 
therefore,  the  dimension  between  the  cen- 
troids  of  the  tensile  and  the  compressive 
forces  equals  jd,  which  equals  (d  —  x). 

Positipn  of  the  Neutral  Axis.  Accord- 
ing to  one  of  the  fundamental  laws  of 
mechanics,  the  sum  of  the  horizontal  ten- 
sile forces  must  be  equal  and  opposite  to 
the  sum  of  the  compressive  forces.  If  the 
very  small  amount  of  tension  furnished 
by  the  concrete  below  the  neutral  axis  is 
ignored,  the  tension  in  the  steel  equals  As  equals  pbds  equals 
the  total  compression  in  the  concrete  which  as  stated  in  Equa- 
tion (1)  equals  %  cbkd.  Therefore 


Fig.  16.  Diagram 
Showing  Side  View 
of  Beam  with  Refer- 
ence to  Deformation 
of  Fibers 


pbds  =  |  cbkd 
ps  ==  \  ck 


(3) 


The  position  of  the  neutral  axis  is  determined  by  the  value  of 
k,  which  is  a  function  of  the  steel  ratio  p  and  the  ratio  of  the 
moduli  of  elasticities  n.  We  must  also  eliminate  s  and  c.  By 
definition,  c  equals  ecEc  and  s  equals  €s  E8  and  n  equals 
ES-+-EC.  Substituting  in  Equation  (3),  we  have 

eE  =  $€Ek  (4). 


REINFORCED  CONCRETE 

TABLE  XI 

Value  of  k  for  Various  Values  of  n  and  p 
(Straight=Line  Formulas) 


57 


n 

P 

.020 

.018 

.016 

.014 

.012 

.010 

.008 

.006 

.004 

.003 

10 
12 
15 
18 
20 
25 
30 
40 

.464 
.493 
.531 

.562 
.580 
.618 
.649 

.698 

.446 
.476 
.513 
.544 
.562- 
.600 
.631 
.679 

.427 
.457 
.493 
.524 
.542 
.580 
.611 
.659 

.407 
.436 
.471 
.501 
.519 
.557 
.588 
.637 

.385 
.412 
.446 
.476 
.493 
.531 
.562 
.611 

.358 
.385 
.418 
.446 
.463 
.500 
.531 
.579 

.328 
.353 
.384 
.412 
.428 
.463 
.493 
.542 

.292 
.314 
.343 
.369 

.384 
.418 
.446 
.493 

.246 
.266 
.291 
.315 
.328 
.358 
.384 
.428 

.216 

.235 
.258 
.279 
.292 
.319 
.344 
.384 

From  the  two  proportional  triangles  in  Fig.  16,  we  may  write 
the  proportion 


kd       d  —  kd 


or  Cft  = 


Substituting  in  Equation  (4)  for  the  ratio  Es  -*-  Ec  its  value  n, 
and  for  ec,  the  value  just  obtained,  we  have 


(5) 


(6) 


Solving  this  quadratic  for  k}  we  have 


k  =  \/2  pn  +  p2n2  —  pn 


Values  of  Ratio  of  Moduli  of  Elasticity.  The  various  values 
for  the  ratio  of  the  moduli  of  elasticity  n  are  discussed  in  the 
succeeding  paragraphs.  The  values  of  k  for  various  values  of 
n  and  p,  have  been  computed  in  Table  XL  Eight  values  have 
been  chosen  for  n}  in  conjunction  with  ten  values  of  p,  varying 
by  0.2  per  cent  and  covering  the  entire  practicable  range  of  p, 
on  the  basis  of  which  values  k  has  been  worked  out  in  the  tabu- 
lar form.  Usually  the  value  of  k  can  be  determined  directly 
from  Table  XL  By  interpolating  between  two  values  in  Table 
XI,  any  required  value  within  the  limits  of  ordinary  practice 
can  be  determined  with  all  necessary  accuracy. 


58  REINFORCED  CONCRETE 

TABLE  XII 

Value  of  ;  for  Various  Values  of  n  and  p 
(Straight=Line  Formulas) 


n 

P 

.020 

.018 

.016 

.014 

.012 

.010 

.008 

.006 

.004 

.003 

10 

12 
15 

18 
20 
25 
30 
40 

.845 
.836 
.823 
.813 

.807 
.794 

.784 
.767 

.851 

.841 
.829 
.819 
.813 
.800 
.790 
.774 

.858 
.848 
.836 
.825 
.819 
.807 
.796 
.780 

.864 

.855 
.843 
.833 

.827 
.814 

.804 
.788 

.872 
.863 
.851 
.841 
.836 
.823 
.813 
.796 

.881 
.872 
.861 
.851 
.846 
.833 
.823 
.807 

.891 

.882 
.872 
.863 
.857 
.846 
.836 
.819 

.903 

.895 
.886 
.877 
.872 
.861 
.851 
.836 

.918 
.911 
.903 

.895 
.891 
.881 
.872 
.857 

.928 
.922 
.914 
.907 
.903 
.894 
.885 
.872 

The  dimension  j  d  from  the  center  of  the  steel  to  the  centroid 
of  the  compression  in  the  concrete  equals  (d  —  x).  Therefore 

:-d~X  d-lkd  1 

3  ~  ~ir     ~d~        zk 

The  corresponding  values  for  j  have  been  computed  for  the 
several  values  of  p  and  n,  as  shown  in  Table  XII.  These  several 
values  for  k  and  j  which  correspond  to  the  various  values  for 
p  and  n  are  shown  in  Fig.  17,  which  is  especially  useful  when 
the  required  values  of  k  and  j  must  be  obtained  by  interpolation. 

Examples.     1.  Assume  w  =  15  and  p  =  .01 ;   how  much  are  k  and  j? 

Solution.  Follow  up  the  vertical  line  on  the  diagram  for  the  steel 
ratio,  p  —  .010,  to  the  point  where  it  intersects  the  k  curve  for  n  =  15; 
the  intersection  point  is  -^  of  one  of  the  smallest  divisions  above  the 
.40  line,  as  shown  on  the  scale  at  the  left ;  each  small  division  is  .020, 
and,  therefore,  the  reading  is  -^  X  .020  =  .018  plus  .400  or  .418,  the 
value  of  k.  Similarly,  the  .010  p  line  intersects  the  j  curve  for  n=15 
at  a  point  slightly  above  the  .860  line,  or  at  .861. 

2.  Assume  n  =  16  and  p  =  .0082  ;    how  much  are  k  and  jf 

Solution.  One  must  imagine  a  vertical  line  (or  perhaps  draw  one) 
at  §  of  a  space  between  the  .0080  and  .0085  vertical  lines  for  p.  This 
line  would  intersect  the  line  for  n  =  15  at  about  .388  ;  and  the  line 
for  n  =  18  at  about  .416;  one-third  of  the  difference  (.028)  or  .009, 
added  to  .388  gives  .397,  the  interpolated  value.  Although  this  is 
sufficiently  close  for  practical  purposes,  the  precise  value  (.398)  mny 
be  computed  from  Equation  (6).  Similarly  the  value  of  ;  may  be 
interpolated  as  .867.  Although  the  values  of  these  ratios  have  been 
computed  to  three  significant  figures  (thousandths),  the  uncertainties 
as  to  the  actual  character  and  strength  of  the  concrete  used  will  make 
it  useless  to  obtain  these  ratios  closer  than  the  nearest  hundredth. 


REINFORCED  CONCRETE 


59 


Theoretically,  there  are  an  indefinite  number  of  values  of  nt 
the  ratio  of  the  moduli  of  elasticity  of  the  steel  and  the  con- 
crete. The  modulus  for  steel  is  fairly  constant  at  about 


Fig.  17.  Curves  Giving  Values  of  fc  and  /  for  Various  Values  of  p  and  n. 

Value.1?  used  for  these  curves  will  be  found  in 

Tables  XII  and  XIII 

29,000,000  or  30,000,000.  The  value  of  the  initial  modulus  for 
stone  concrete  varies,  according  to  the  quality  of  the  concrete, 
from  l,500,000\o  3,000,000.  An  average  value  for  1:2:4 


60  REINFORCED  CONCRETE 

TABLE  XIII 
Modulus  of  Elasticity  of  Some  Grades  of  Concrete 


KIND  OF  CONCRETE 

AGE 
(Days) 

MIXTURE 

EC 

n 

Cinder  .      *  * 

30 

1  -2  -4 

1  200  000 

25 

30 

1  '3  -6 

2  000  000 

15 

10 

1  -2  *4 

2*000*000 

15 

Broken  stone  

30 

1:2:4 

2!500!000 

12 

cinder  concrete  is  about  1,200,000.  Some  experimental  values 
for  stone  concrete  have  fallen  somewhat  lower  than  1,500,000, 
while  others  have  reached  4,000,000  and  even  more.  We  may 
use  the  values  in  table  XIII  with  the  constant  value  of 
30,000,000  for  the  steel. 

Percentage  of  Steel.  The  previous  calculations  have  been 
made  as  if  the  percentage  of  the  steel  might  be  varied  almost 
indefinitely.  While  there  is  considerable  freedom  of  -choice, 
there  are  limitations  beyond  which  it  is  useless  to  pass;  and 
there  is  always  a  most  economical  percentage,  depending  on  the 
conditions.  We  must,  therefore,  determine  p  in  terms  of  c,  sf 
and  n.  Substituting  in  Equation  (3),  the  value  of  k  in  Equation 
(6)  we  have 


which  may  be  reduced  to 


x  c 
2       8 


cn 


(8) 


(s  +  en) 

This  equation  shows  that  we  cannot  select  the  percentage  of 
steel  at  random,  since  it  evidently  depends  on  the  selected 
stresses  for  the  steel  and  concrete  and  also  on  the  ratio  of 
their  moduli.  For  example,  consider  a  high-grade  concrete— 
1:2:4— whose  modulus  of  elasticity  is  considered  to  be  2,500,- 
000,  and  which  has  a  working  compressive  stress  c  of  600 
pounds,  which  we  may  consider  in  conjunction  with  a  tensile 
stress  of  16,000  pounds  in  the  steel.  The  values  of  c,  s,  and  n 
are  therefore  600,  16,000,  and  12,  respectively.  Substituting 
these  values  in  Equation  (8)  we  compute  p  equal  to  .0058. 


REINFORCED  CONCRETE  61 

This  theoretical  percentage  is  not,  necessarily,  the  most 
economical  or  the  most  desirable  percentage  to  use.  For  a  beam 
of  given  size,  some  increase  of  strength  may  be  obtained  by 
using  a  higher  percentage  of  steel ;  or  for  a  given  strength,  or 
load  capacity,  the  depth  may  be  somewhat  decreased  by  using 
a  higher  percentage  of  steel.  The  decrease  in  height,  making 
possible  a  decrease  in  the  total  height  of  the  building  for  a 
given  clear  headroom  between  floors,  may  justify  the  increase 
in  the  percentage  of  steel,  but  that  is  determined  by  considera- 
tions of  economy. 

Example.  What  is  the  theoretical  percentage  of  steel  for  ordinary 
stone  concrete  when  n  =  15,  c  =  650,  and  s  =  18,000?  Ans.  .0063 

Resisting  Moment.  The  moment  which  resists  the  action 
of  the  external  forces  is  evidently  measured  by  the  product  of 
the  distance  from  the  center  of  gravity  of  the  steel  to  the 
centroid  of  compression  of  the  concrete,  times  the  total  com- 
pression of  the  concrete,  or  times  the  tension  in  the  steel.  As  the 
compression  in  the  concrete  and  the  tension  in  the  steel  are 
equal,  it  is  only  a  matter  of  convenience  to  express  this  product 
in  terms  of  the  tension  in  the  steel.  Therefore,  adopting  the 
notation  already  mentioned,  we  have  the  formula 

M=As(jd)  (9) 

But  since  the  computations  are  frequently  made  in  terms  of 
the  dimensions  of  the  concrete  and  of  the  percentage  of  the 
reinforcing  steel,  it  may  be  more  convenient  to  write  the 
equation 

M=(pbds)jd  (10) 

From  Equation  (1)  we  have  the  total  compression  in  the  con- 
crete. Multiplying  this  by  the  distance  from  the  steel  to  the 
centroid  of  compression  jd,  we  have  another  equation  for  the 
moment 

M  =  ^(cbkd)jd  (11) 

When  the  percentage  of  steel  used  agrees  with  that  computed 
from  Equation  (8),  then  Equations  (10)  and  (11)  will  give 


62  REINFORCED  CONCRETE 

TABLE  XIV 
Value  of  p  for  Various  Values  of  (s-hc)  and  n 

Formula:     p  =  —  X—  ( —  — )  ,  in  which  R  =  (s-^c) 
2      R   \R  -j-  /i/ 


n 

' 

(S-i-C) 

10 

12 

15  , 

18 

20 

25 

30 

40 

10.0 

.0250 

.0273 

.0300 

.0321 

.0333 

.0357 

.0375 

.0400 

12.5 

.0178 

.0196 

.0218 

.0236 

.0246 

.0267 

.0282 

.0304 

15.0 

.0133 

.0148 

.0167 

,  .0182 

.0190 

.0208 

.0222 

.0242 

17.5 

.0104 

.0116 

.0132 

.0145 

.0152 

.0168 

.0180 

.0191) 

20.0 

.0083 

.0094 

.0107 

.0118 

.0125 

.0139 

.0150 

.0167 

25.0 

.0057 

.0065 

.0075 

.0084 

.0089 

.0100 

.0109 

.0123 

30.0 

.0042 

.0048 

.0056 

.0062 

.0067 

.0076 

.0083 

.0095 

40.0 

.0025 

.0029 

.0034 

.0039 

.0042 

.0048 

.0054 

.00621 

50.0 

.0017 

.0019 

.0023 

.0026 

.0029 

.0033 

.0037 

.0044 

identically  the  same  results;  but  when  the  percentage  of  steel  is 
selected  arbitrarily,  as  is  frequently  done,  then  the  proposed 
section  should  be  tested  by  both  equations.  When  the  percent- 
age of  steel  is  larger  than  that  required  by  Equation  (8),  the 
concrete  will  be  compressed  more  than  is  intended  before  the 
steel  attains  its  normal  tension.  On  the  other  hand,  a  lower 
percentage  of  steel  will  require  a  higher  unit  tension  in  the 
steel  before  the  concrete  attains  its  normal  compression.  If  the 
discrepancy  between  the  percentage  of  steel  assumed  and  the 
true  economical  value  is  very  great,  the  stress  in  the  steel,  or 
the  concrete,  may  become  dangerously  high  when  the  stress  in 
the  other  element,  on  which  the  computation  may  have  been 
made,  is  only  normal. 

Working  Values  for  the  Ratio  of  the  Steel  Tension  to  the 
Concrete  Compression.  It  is  often  more  convenient  to  obtain 
working  values  from  tables  or  diagrams  rather  than  to  compute 
them  each  time  from  equations. 

If  Equation  (8)  is  solved  for  several  combinations  of  values 
of  (s  ~-  c)  and  n,  we  have  the  values  as  tabulated  in  Table  XIV. 
These  values  are  also  shown  in  Fig.  18.  For  other  combinations 
than  those  used  in  Table  XIV,  the  values  of  p  may  be  obtained 
with  great  accuracy  provided  that  (s  -*-  c)  corresponds  with 
some  curve  already  on  the  diagram.  If  it  is  necessary  to  inter- 


REINFORCED  CONCRETE 


63 


.QQK 


/O       /£      ?O      ?5      30 

Fig.  18.     Curves  Showing  the  Relation  of   (s-^-c)    to  p  and  11 


64  REINFORCED  CONCRETE 

polate  for  some  value  of  (s-*-c)  of  which  the  curve  has  not 
been  drawn,  it  must  be  recognized  that  the  space  between  the 
curves  increases  rapidly  as  (s  -*-  c)  is  smaller.  For  example, 
to  interpolate  for  (s  -5-  c)  =  32,  the  point  must  be  below  the 
30  curve  by  considerably  more  than  0.2  of  the  interval  between 
the  30  and  40  curve. 

The  relative  elasticities  n  of  various  grades  of  steel  and 
concrete  are  usually  roughly  proportional  to  the  relative  work- 
ing values,  as  expressed  by  (s-*-c).  In  other  words,  if  n  is 
large,  (s  -+-  c)  is  correspondingly  large  unless  the  working  value 
for  s  or  for  c  is  for  some  reason  made  abnormally  low.  There- 
fore, there  will  be  little  if  any  use  for  the  values  given  in  the 
lower  left-hand  and  upper  right-hand  corners  of  Table  XIV. 

Determination  of  Values  for  Frequent  Use.  The  moment  of 
resistance  of  a  beam  equals  the  total  tension  in  the  steel,  or  the 
total  compression  in  the  concrete  (which  are  equal)  times  jd. 
Therefore,  we  have  the  choice  of  two  values,  as  given  in  Equa- 
tions (9)  to  (11). 


Ms  =  As  (jd)  =  (pbds)  jd 

If  the  theoretical  percentage  p  has  already  been  determined 
from  Equation  (8),  then  either  equation  may  be  used,  as  is  most 
convenient,  since  the  two  will  give  identical  results.  If  the  per- 
centage has  been  arbitrarily  chosen,  then  the  least  value  must 
be  determined,  as  was  described  previously.  For  any  given  steel 
ratio  and  any  one  grade  of  concrete,  the  factors  i-  ckj  or  psj 
are  constant  and  Equation  (12)  may  be  written 

Mc  =  Rcbd2 
Ms  =  Rsbd2 
or,  in  general, 

M  =  Rbd2 

when  the  theoretical  percentage  of  steel  is  used.    Diagrams  for 
quickly  determining  R  are  given  later. 

For  1:2:4  concrete,  using  n  =  15,  and  with  a  working  value 


REINFORCED  CONCRETE  65 

for  c  =  600,  and  s  =  16,000,  we  find  from  Equation  (8)  that 
the  percentage  of  steel  equals 

_1      600  600  X  15 

P      2  16,000       (600  X  15)  +  16,000 

From  Table  XI  we  find  by  interpolation  that,  for  n  =  15  and 
p  =  .00675,  k  =  .360.  Then,  from  Equation  (2), 

x  =  \kd  =  .120  d        and  j  =  .880 

o 

> 

Substituting  these  values  in  either  formula  of  Equation  (12), 
we  have 

M  =  95  bd2 

The  percentage  of  steel  computed  from  Equation  (8)  has 
been  called  the  theoretical  percentage,  because  it  is  the  percent- 
age which  will  develop  the  maximum  allowed  stress  in  the  con- 
crete and  the  steel  at  the  same  time,  or  by  the  loading  of  the  beam 
to  some  definite  maximum  loading.  The  real  meaning  of  this  is 
best  illustrated  by  a  numerical  example  with  another  percentage. 
Assume  that  the  percentage  of  steel  is  exactly  doubled,  or  that 
p  equals  2  X  .00675  =  .0135.  From  Table  XI  for  n  =  15,  and 
p  =  .0135  we  find  k  =  .465 ;  x  =  .155  d ;  and  j  =  .845.  Substi- 
tuting these  values  in  both  forms  of  Equation  (12),  we  have 

Mc  =  118  bd2 
M8  =  183  bd2 

The  interpretation  of  these  two  equations,  and  also  of  the  equa- 
tion found  above  (M  =  95bd2),  is  as  follows:  Assume  a  beam 
of  definite  dimensions  b  and  d,  made  of  concrete  whose  modulus 
of  elasticity  is  -Jg-  that  of  the  modulus  of  elasticity  of  the  rein- 
forcing steel;  assume  that  it  is  reinforced  with  steel  having  a 
cross-sectional  area  equal  to  .00675  bd.  Then,  when  the  beam 
is  loaded  with  a  load  which  will  develop  a  moment  of  95  bd2, 
the  tension  in  the  steel  will  equal  16,000  pounds  per  square  inch, 
and  the  compression  in  the  concrete  will  equa-1  600  pounds  per 
square  inch  at  the  outer  fiber.  Assume  that  the  area  of  the 
steel  is  exactly  doubled.  One  effect  of  this  is  to  lower  the  neutral 
axis— k  is  increased  from  .360  to  .465— and  more  of  the  concrete 


66  REINFORCED  CONCRETE 

is  available  for  compression.  The  load  may  be  increased  about 
24  per  cent,  or  until  the  moment  equals  IIS  bd2,  before  the  com- 
pression in  the  concrete  reaches  600  pounds  per  square  inch. 
Under  these  conditions  the  steel  has  a  tension  of  about  10,340 
pounds  per  square  inch,  and  its  full  strength  is  not  utilized. 
If  the  load  were  increased  until  the  moment  were  183  bd2,  then 
the  steel  would  be  stressed  to  16,000  pounds  per  square  inch, 
but  the  concrete  would  be  compressed  to  about  930  pounds, 
which  would,  of  course,  be  unsafe  with  such  a  grade  of  coneretev 
If  the  compression  in  the  concrete  is  to  be  limited  to  600  pounds 
per  square  inch,  then  the  load  must  be  limited  to  that  which  will 
give  a  moment  of  118  bd2.  Even  for  this  the  steel  is  doubled  if 
the  load  is  to  be  increased  24  per  cent.  Whether  this  is  justifi- 
able, depends  on  several  circumstances— the  relative  cost  of 
steel  and  concrete,  the  possible  necessity  for  keeping  the  dimen- 
sions of  the  beam  within  certain  limits,  etc.  Usually,  a  much 
larger  ratio  of  steel  than  0.675  per  cent  is  used ;  1.0  per  cent  is 
far  more  common;  but  in  the  latter  case  the  strength  of  the 
steel  cannot  be  fully  utilized  unless  the  concrete  can  stand  high 
compression.  A  larger  value  of  n  will  indicate  higher  values  of 
k,  which  will  indicate  higher  moments;  but  n  cannot  be  selected 
at  pleasure.  It  depends  on  the  character  of  the  concrete  used ; 
and,  with  Es  constant,  a  large  value  of  n' means  a  small  value 
for  Ec,  which  means  also  a  small  value  for  c,  the  permissible 
compression  stress.  Whenever  the  percentage  of  steel  is  greater 
than  the  theoretical  percentage,  as  is  usual,  then  the. upper  of  the 
two  formulas  of  Equation  (12)  should  be  used.  When  in  doubt, 
both  should  be  tested,  and  that  one  giving  the  lower  moment 
should  be  used. 

When  p  =  .0075,  n  =  15,  c  =  600,  and  s  =  16,000,  'as  before, 
we  have  k  =  .374,  x  =  .125  d,  and  j  =  .875.  Then,  since  p  is 
greater  than  the  theoretical  value,  we  use  the  upper  formula  of 
Equation  (12)  and  have 

M  =  98  bd2 

Examples.  1.  What  is  the  working  moment  for  n  slab  with  5-inch 
thickness  to  the  steel,  the  concrete  having  the  properties  described 
above? 


REINFORCED  CONCRETE  67 

ftolution.  Lot  6  =  12  inches.  Then  Jlf  =  98  X  12  X  25  =  29,400  inch- 
pounds,  the  permissible  moment  on  a  section  12  inches  wide. 

2.  A  slab  having  a  span  of  8  feet  is  to  support  a  load  of  150  pounds 
per  square  foot.  The  concrete  is  to  be  as  described  above,  and  the 
percentage  of  steel  is  to  be  0.75.  What  is  the  required  thickness  d  to 
the  steel  ? 

Solution.  Allowing  70  pounds  per  square  foot  as  the  estimated 
weight  of  the  slab  itself,  the  total  load  is  220  pounds  per  square  foot. 
A  strip  12  inches  wide  has  an  area  of  8  square  feet,  and  the  total  load 
is  1,760  pounds.  Assuming  the  slab  as  free-ended,  the  moment  is 

5  Wl  =  |  X  1,760  X  96  =  21,120  in.-lb. 
For  a  strip  12  inches  wide,  6  =  12  inches  and 

M  =  98  X  12  X  d2  =  l,176d8  =  21,120 
d2— 17.96 
d  =  4.24  in. 

Then,  allowing  one  inch  of  concrete  below  the  steel,  the  total  thickness 
of  the  slab  would  be  5J  inches  and  its  weight,  allowing  12  pounds  per 
square  foot  per  inch  of  depth,  would  be  about  68  pounds  per  square 
foot,  thus  agreeing  safely  with  the  estimated  allowance  for  dead  load. 
If  the  computed  thickness  and  weight  had  proved  to  be  materially 
more  than  the  original  allowance,  another  calculation  would  be  neces- 
sary, assuming  a  somewhat  greater  dead  load.  This  increase  of  dead 
load  would  of  itself  produce  a  somewhat  greater  moment,  but  the 
increased  thickness  would  develop  a  greater  resisting  moment.  A  little 
experience  will  enable  one  to  make  the  preliminary  estimate  so  close 
to  the  final  that  not  more  than  one  trial  calculation  should  be 
mecessary. 

PRACTICAL  CALCULATION  AND  DESIGN  OF  BEAMS 
AND  SLABS 

Tables  for  Slab  Computations.  The  necessity  of  computing 
frequently  the  required  thickness  of  slabs  renders  very  useful 
the  data  given  in  Table  XV,  which  has  been  worked  out  on  the 
basis  of  several  combinations  of  values  of  c  and  s.  Municipal 
building  laws  often  specify  the  unit  values  which  must  be  used 
and  even  the  moment  formula.  For  example,  slabs  are  usually 
continuous  over  beams  and  even  the  wall  ends  of  slabs  are  so 
restrained  at  the  wall  that  the  working  moment  is  considerably 
less  than  Wl  -*-  8  and,  therefore,  the  formula  Wl  -*- 10  is  spe- 
cifically permitted  in  many  municipal  regulations.  Table  XV 
is  computed  on  that  basis,  but  the  tabulated  unit  loads  may  be 
very  easily  changed  to  the  basis  of  Wl  -*-  8  or  Wl  -*- 12.  It 
should  be  noted  that  the  unit  loads  given  in  Table  XV  include 
the  slab  weight,  which  must,  therefore,  be  subtracted  before  the 


68 


REINFORCED  CONCRETE 


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I-H  ^H  r-t  (N  <M  CO  >O  O  00 


c^  ^  o  »o  c^  -H  -H    • 

(N  CO  ^  iO  t^  O  O     • 


iO  CO  CO  CO  CO 

IOCOOO.-H 


REINFORCED  CONCRETE  71 

net  live  load  is  known.  In  the  last  column  are  shown  the  unit 
weights  of  various  slab  thicknesses  on  the  basis  of  108  pounds 
per  cubic  foot  for  cinder  concrete  and  144  pounds  per  cubic 
foot  for  stone  concrete.  These  subtractive  weights  may  need 
to  be  altered  if  a  concrete  of  different  weight  is  used,  or  if  an 
extra  top  coat  of  concrete,  which  cannot  be  considered  as  struc- 
turally a  part  of  the  slab,  is  laid  on  afterward.  The  "thickness 
of  concrete  below  steel"  is  such  as  is  approved  by  good  practice, 
but  in  case  municipal  regulations  or  other  reasons  should  require 
other  thicknesses  of  concrete  below  the  "steel,  Table  XV  may  still 
be  used  by  considering  the  effective  thickness  d  and  by  varying, 
as  need  be,  the  subtractive  weight  of  the  slab  to  determine  the 
net  load.  The  blanks  in  the  upper  right-hand  corner  of  each 
section  of  the  table  indicate  that  for  those  spans  and  slab  thick- 
nesses the  slabs  cannot  safely  carry  their  own  weight  and  that 
even  the  weights  nearest  the  blanks  are  so  small  that,  after  sub- 
tracting the  slab  weights,  the  remainders  are  too  small  for  prac- 
tical working  floor  loads,  or  even  roof  loads.  The  blanks  in  the 
lower  left-hand  corner  of  each  section  of  the  table  indicate  that 
for  these  combinations  of  span,  load,  and  slab  thickness,  the 
shearing  strength  would  be  insufficient  for  the  load  which  its 
transverse  strength  would  enable  it  to  carry  and  that,  therefore, 
although  those  slabs  would  carry  a  great  load,  those  combina- 
tions of  span  and  slab  thickness  are  uneconomical  and  should 
not  be  used. 

Examples.  1.  Using  stone  concrete  such  that  c  =  600,  n  =  15,  and 
s  —  10,000,  and  with  a  required  working  load  of  200  pounds  per  square 
foot,  what  span  may  he  chosen? 

Solution.  This  requires  Section  3  of  Table  XV.  We  note  that  an 
8-inch  slab  on  a  span  of  12  feet  will  carry  300  pounds  per  square  foot 
gross,  or  204  pounds  net,  which  is  substantially  what  is  required. 
Another  combination  would  be  a  7-inch  slab  with  a  span  between  10 
and  11  feet.  To  interpolate,  subtract  84,  the  unit  slab  weight,  from 
314  and  from  259,  giving  230  and  175.  It  should  be  noted  that  the 
difference  388  —  314  =  74,  is  greater  than  the  difference  314  —  259 
=  55,  which  in  turn  is  greater  than  the  difference  259  —  218  =  41. 
From  this  we  may  know,  without  precise  calculations,  that  the  value 
for  the  span  10  feet  6  inches  must  be  such  that  the  difference  between 
230  (net  value)  and  the  net  value  for  10  feet  6  inches  must  be  greater 
than  the  difference  between  this  net  value  and  175,  the  net  value  for 
an  11-foot  span.  230  —  200  =  30  and  200  —  175  =  25.  Therefore,  a 


72  REINFORCED  CONCRETE 


of  10  feet  6  inches  is  very  close  to  the  theoretical  value — close 
enough  for  practical  purposes.  Whether  an  8-inch  slab  with  12-foot 
span  or  a  7-inch  slab  with  10-foot-6-inch  span  is  the  more  economical 
or  desirable  depends  on  other  conditions,  one  of  which  is  the  span  of 
the  beams.  This  will  be  considered  later. 

2.  Find   the   npan,   assuming   the   same   data   as  above,   except   that 
municipal  regulations  require  at  least  1|  inches  of  concrete  below  the 
steel  and  also  require  using  the  formula  Wl  -=-  8. 

Solution.  An  8-inch  slab  with  1J  inches  of  concrete  under  the  steel 
will  be  85  inches  thick  and  will  weigh  99  pounds  per  square  foot.  On 
the  11-foot  span  the  total  load,  after  subtracting  20  per  cent,  will  be 
286  pounds  and,  after  subtracting  99,  will  leave  187  pounds  net. 
Similarly,  the  net  load  on  the  10-foot  span  is  247  pounds.  200  —  187 
—  13,  and  247  — 187  =  60;  13  is  nearly  one-fourth  of  60  and,  there- 
fore, the  interpolated  span  is  about  one-fourth  of  the  interval  from 
11  feet  back  to  10  feet,  or  10  feet  9  inches.  The  net  effect  of  adding 
the  extra  concrete  below  the  steel  and  using  Wl+-  8  instead  of  Wl  -=-  10, 
therefore,  reduces  the  span  of  the  8-inch  slab  from  12  feet  to  10  feet 
9  inches.  A  similar  computation  could  be  made  for  a  7-inch  slab — 
actual  thickness  7J  inches. 

3.  Assume  a  slab   made  of  1 :  2.5  :  5   concrete ;    the  span   has  been 
determined    already   as    6    feet ;     the    floor    is    to   be   covered   with    2 
inches  of  cinder-concrete  fill   between  the   wood  sleepers   and   a  wood 
floor,  weighing  23  pounds  per  square  foot ;    the  live  load  is  to  be  150 
pounds  per  square  foot.     Required,  the  slab  thickness. 

Solution.  For  such  concrete,  use  Section  2,  Table  XV.  150  +  23  = 
173 ;  and  adding  a  trial  figure  of  50  pounds  for  the  unit  weight  of 
the  slab,  we  have  223  as  the  total  load.  Under  6-feet  span  we  find 
192  for  a  4-inch  slab  and  261  for  a  4|-inch  slab  ;  4  inches  is  too  thin 
and  4J  somewhat  needlessly  thick.  Since  223  is  nearer  to  192  than  to 
261,  we  may  economize  by  cutting  the  thickness  to  44  inches.  The 
detail  of  the  interpolation,  elaborated  in  Example  2,  shows  this  to  be 
justifiable.  The  required  area  of  steel  for  the  4|-inch  slab  is  found  by 
interpolation,  between  .223  and  .260,  or  .242  square  inch — the  area  of 
steel  in  12  inches  of  width  of  slab.  This  is  .02  square  inch  per  inch 
of  width ;  a  |-inch  square  bar  has  an  area  of  .1406  square  inch ; 
therefore,  such  bars  spaced  7  inches  apart  will  fulfil  the  requirements. 

Table  for  Computation  of  Simple  Beams.  In  Table  XVI 
has  been  computed,  for  convenience,  the  working  total  load 
(including  the  weight  of  the  beam)  on  rectangular  beams  one 
inch  wide  and  of  various  depths  and  spans.  For  other  widths 
of  beams,  multiply  the  tabular  load  by  the  width  of  the  beam 
in  inches.  Table  XVI  is  based  on  a  grade  of  concrete  such  that 
M  equals  100  bd2 ;  for  any  other  grade  of  concrete,  determine 
the  corresponding  factor  of  bd2,  or,  in  other  words,  Equa- 
tion (12),  compute  the  value  of  \  ckj,  or  of  psj,  whichever  is 
less.  Multiply  the  tabular  load  by  the  percentage  of  that  factor 


REINFORCED  CONCRETE 


73 


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— |<N       (MCO-* 


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lO  IO  t^-  ^H  O  «f 
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t^OOO        O-HCM        COTTI.O 


74  REINFORCED  CONCRETE 

to  100.  The  concrete  of  Section  5,  Table  XV,  has  the  factor 
100  and  if  such  concrete  is  used,  no  percentage  multiplication 
is  necessary.  The  blanks  in  the  upper  right-hand  corner  of 
Table  XVI  are  similar  to  the  corresponding  blanks  in  Table 
XV — the  beams  cannot  safely  carry  their  own  weight.  And, 
as  before,  the  values  immediately  adjacent  to  the  blanks  are  of 
little  or  no  use,  since  the  possible  load,  after  deducting  the 
weight  of  the  beam,  would  be  too  small  for  practical  purposes. 
The  values  in  the  lower  left-hand  corner  should  be  used  with 
great  caution.  Many  of  the  beams  of  such  relative  span  and 
depth  would  fail  from  diagonal  shear  long  before  the  tabulated 
loads  were  reached.  But,  since  the  liability  to  failure  from 
diagonal  shear  is  dependent  on  the  nature  of  the  web  reinforce- 
ment, the  line  of  demarcation  is  not  easily  drawn,  as  was  done 
in  Table  XV. 

Examples.  1.  Assume  the  concrete  described  in  Section  3,  Table 
XV,  which  has  the  factor  95.  How  much  load  will  be  carried  by  a 
beam  of  such  concrete,  when  the  beam  is  8  inches  wide,  16  inches 
effective  depth,  and  18  feet  span? 

Solution.  From  Table  XVI,  under  18  feet  span  and  opposite  16 
inches  effective  depth,  we  find  948,  the  load  for  a  beam  one  inch  wide. 
An  8-inch  beam  will  carry  8  times  948,  or  7,584  pounds.  95  per  cent 
of  7,584  is  7,205  pounds,  the  load  for  that  particular  grade  of  concrete. 
The  weight  of  the  concrete,  assuming  a  total  depth  of  18  inches,  is 

1  x  1|  x  18  X  144  =  2,592.    Deducting   this   from    7,205,   we   have   the 

net  load  as  4,613  pounds. 

2.  Assume  that  c  =  500,  s  =  16,000,  n  =  12,  and  p  =  .006.  How  much 
load  will  be  carried  by  a  beam  6  inches  wide,  12  inches  effective  depth, 
and  14  feet  span? 

Solution.  From  the  percentage  diagram  on  page  63,  we  see  that 
for  8-±-c  —  32  and  for  n  =  12,  p  =  .0043  ;  and  since  this  is  less  than 
the  chosen  steel  ratio  .006,  we  must  use  the  first  part  of  Equation  (12). 
For  n  =  12  and  for  p  =  .006,  k  =  .314  and  ;  =  .895.  Then  \  ckj  =  250 
X  .314  X  .895  =  70,  the  factor  of  6d2.  The  load  on  a  beam  one  inch 
wide,  12  inches  effective  depth,  and  14  feet  span  is  685  pounds.  For  6 
inches  wide  it  would  be  4,110  pounds.  70  per  cent  of  this  is  2,877 

/>  1  -i 

pounds.  The  weight,  allowing  2  inches  below  the  steel,  is  f2  X  12 
X  14  X  144  =  1,176  pounds.  The  not  load  is,  therefore,  4,110  —  1,176  = 
2,934  pounds. 

Bonding  Steel  and  Concrete.  Resistance  to  SUppiny  of 
Steel  in  Concrete.  The  previous  discussion  has  considered 


REINFORCED  CONCRETE  75 

merely  the  tension  and  compression  in  the  upper  and  lower 
sides  of  the  beam.  A  plain,  simple  beam  resting  freely  on  two 
end  supports  has  neither  tension  nor  compression  in  the  fibers 
at  the  ends  of  the  beam.  The  horizontal  tension  and  compres- 
sion, found  at  or  near  the  center  of  the  beam,  entirely  disappear 
by  the  time  the  ends  of  the  beam  are  reached.  This  is  done  by 
means  of  the  intermediate  concrete  which  transfers  the  tensile 
stress  in  the  steel  at  the  bottom  of  the  beam  to  the  compression 
fibers  in  the  top.  This  is,  in  fact,  the  main  use  of  the  concrete 
in  the  lower  part  of  the  beam. 

It  is,  therefore,  necessary  that  the  bond  between  the  concrete 
and  the  steel  shall  be  sufficiently  great  to  withstand  the  tendency 
to  slip.  The  required  strength  of  this  bond  is  evidently  equal 
to  the  difference  in  the  tension  in  the  steel  per  unit  of  length. 
For  example,  suppose  that  we  are  considering  a  bar  1  inch 
square  in  the  middle  of  the  length  of  a  beam.  Let  the  bar  be 
under  an  actual  tension  of  15,000  pounds  per  square  inch. 
Since  the  bar  is  1  inch  square,  the  actual  total  tension  is  15,000 
pounds.  Suppose  that,  at  a  point  1  inch  beyond,  the  moment  in 
Hie  beam  is  so  reduced  that  the  tension  in  the  bar  is  14,900 
pounds  instead  of  15,000  pounds.  This  means  that  the  differ- 
ence of  pull  (100  pounds)  has  been  taken  up  by  the  concrete. 
The  surface  of  the  bar  for  that  length  of  1  inch  is  4  square 
inches.  This  will  require  an  average  adhesion  of  25  pounds  per 
square  inch  between  the  steel  and  the  concrete  in  order  to  take 
up  this  difference  of  tension.  The  adhesion  between  concrete 
and  plain  bars  is  usually  considerably  greater  than  this,  and 
there  is,  therefore,  but  little  question  about  the  bond  in  the  center 
of  the  beam.  But  near  the  ends  of  the  beam,  the  change  in  ten- 
sion in  the  bar  is  far  more  rapid,  and  the  question  of  the  bond 
then  becomes  important. 

Virtue  of  Deformed  Bars.  The  fact  that  the  adhesion  of  the 
concrete  to  the  steel  is  a  critical  feature  under  some  conditions, 
called  attention  to  the  desirability  of  using  deformed  bars,  which 
furnish,  a  mechanical  bond.  Deformed  bars  have  a  variety  of 
shapes;  and  since  they  are  not  prismatic,  it  is  evident  that,  apart 
from  adhesion,  they  cannot  be  drawn  through  the  concrete  with- 


76  REINFORCED  CONCRETE 

TABLE  XVII 

Bond  Adhesion  of  Plain  and  Deformed  Bars  per 
Inch  of  Length 

Basis  J    75  Ib<  adnes.ion  Per  square  inch  for  plain  bars 

I  125  ib.  adhesion  per  square  inch  for  deformed  bars 
For  any  other  unit  basis,  multiply  surface  (column  2  or  3)  by  unit 


SIZE 

SURFACE 
(Square  Inches 

BOND  ADHESION 
(Pounds  per  Lineal  Inch) 

j 

OP  BAB 
(Inches) 

per  Lineal  Inch) 

Plain  Bars             Deformed  Bars 
at  75                          at  125 

Square 

Round 

Square 

Round 

Square 

Round 

i 

1.00             0.785 

75 

59 

125 

98 

A 

1.25 

0.982 

94 

74 

156 

123 

i 

1.50 

1.178 

112 

88 

187 

147 

A 

1.75 

1.375 

131 

103 

219 

172 

1 

2.00 

1.571 

150 

118 

250 

196 

i 

2.50 

1.964 

187 

147 

312 

245 

1 

3.00 

2.356 

225 

177 

375 

294 

§ 

3.50 

2.749 

262 

206 

437 

344 

i 

4.00 

3.142 

300 

236 

500 

393 

li 

4.50 

3.534 

337 

265 

562 

442 

if 

5.00 

3.927             375 

324 

625 

491 

out  splitting  or  crushing  the  concrete  immediately  around  the 
bars.  The  choice  of  form  is  chiefly  a  matter  of  designing  a  bar 
which  will  furnish  the  greatest  resistance,  and  which  at  the  same 
time  is  not  unduly  expensive  to  manufacture.  Impartial  tests 
have  shown  that,  even  under  conditions  which  are  most  favor- 
able to  the  plain  bars,  the  deformed  bars  have  an  actual  hold  in 
the  concrete  which  is  from  50  to  100  per  cent  greater  than  that 
of  plain  bars.  It  is  unquestionable  that  age  will  increase  rather 
than  diminish  the  relative  inferiority  of  plain  bars. 

The  specifications  of  the  American  Railway  Engineering 
Association,  adopted  in  1910,  allow  SO  pounds  per  square  inch 
of  surface  for  plain  bars,  40  for  drawn  wire,  and  from  100  to 
150  for  deformed  bars  "depending  upon  form".  Municipal 
regulations  frequently  limit  the  adhesion  to  75  pounds,  without 
any  mention  of  deformed  bars  or  of  any  extra  allowable  ad- 
hesion if  they  are  used.  The  adhesion  is  of  special  importance 


REINFORCED  CONCRETE 


77 


in  short  but  deep,  heavily  loaded  beams.  It  is  frequently  diffi- 
cult to  obtain  the  necessary  adhesion  with  an  allowance  of  only 
75  pounds  per  square  inch.  Refer  to  Table  XVII. 

Computation  of  Bond  Required  in  Bars.  From  theoretical 
mechanics,  we  learn  that  the  total  shear  V  at  any  section  equals 
the  difference  in  moment  for  the  ends  of  a  section  of  infinitesi- 
mal length.  This  may  be  seen  from  Fig.  19  where  T  is  tension  in 
steel  at  left  end  of  section  and  toward  the  center  of  the  beam; 
T'  is  tension  in  steel  at  right  end  of  section ;  then  T  —  T'  is  the 
difference  in  tension,  which  is  the  amount  of  tension  taken  up 
by  the  concrete  in  the  length  x.  Then  (T  —  T'}  jd  is  the  dif- 
ference of  moment  in  the  unit  distance  x.  But  by  taking 
moments  about  a,  we  have  the  following  expression : 

Vx=(T-T'}jd 
from  which 


If  x  is  considered  to  be  the  unit 
length— say  one  inch— then  the  bond 
adhesion  on  all  the  bars  will  be  V~^~jd. 
If  we  call  v  the  unit  horizontal  shear, 
and  the  width  t)f  the  beam  b,  then 


v  =  V  -  bjd 


(13) 


Fig.  19.    Diagram  for  Cal- 
culating Moments  of 
Inertia  in  a  Bar 


Illustrative  Example.  Assume  an 
8-foot  beam,  uniformly  loaded  to  its 
capacity,  with  an  effective  depth  d  = 

16  inches,  width  b  =  8  inches,  c  =  600,  s  =  16,000,  and  n  =  15. 
Then  p  =  .00675,  k  =  .360,  j  =  .880,  and  A  =  16  X  8  X  .0067  = 
0.86  square  inch.  This  area  may  be  obtained  from  three  f-inch 
round  bars,  each  of  which  will  have  a  cross-sectional  area  of  .30 
square  inch  and  circumference  of  1.96  inches,  which  means  an 
adhesion  area  of  5.88  square  inches  per  inch  of  length  of  the 
three  bars.  M  equals  95  bd2  or  194,560  inch-pounds  equals 
Wl  +  8.  Since  Z  =  96  inches,  then  W  =  16,213,  and  V,  the 
maximum  total  shear,  is  one-half  of  this  or  8,107  pounds.  At  a 
point  one  foot  from  the  center  the  shear  will  be  one-fourth  of 


78  REINFORCED  CONCRETE 

the  maximum  shear,  or  2,027  pounds;  dividing1  this  by  jd,  or 
.880  X  16,  we  have  144  pounds,  the  required  bond  adhesion  at 
that  point.  Dividing  this  by  the  area,  5.88,  we  have  24  pounds 
per  square  inch,  the  adhesion  stress,  which  is  amply  safe. 

At  the  abutment  tlie  shear  is  8,107  pounds;  dividing  this  by 
jd,  or  .880  X  16,  we  have  575  pounds,  the  required  total  adhe- 
sion. 575  -*-  5.88  =  98,  the  required  unit  adhesion.  This  is 
greater  than  the  permissible  unit  adhesion  of  plain  bars,  and 
greater  than  the  uniform  figure  (75)  given  in  so  many  municipal 
building  codes,  although  not  greater  than  that  which  deformed 
bars  can  safely  carry. 

Another  possible  solution  of  the  problem,  although  one  with 
some  loss  of  economy,  would  be  to  use  four  ^-inch  square  bars, 
whose  total  cross-sectional  area  would  be  one  square  inch  (in- 
stead of  0.86)  and  whose  superficial  area  per  inch  of  length 
would  be  8  square  inches.  578  -*-  8  =  72  pounds  per  square 
inch.  This  is  within  the  specified  limit  for  plain  bars.  Strictly 
speaking,  this  would  not  be  the  precise  figure,  since  the  added 
percentage  of  steel  would  slightly  decrease  j  and  therefore 
slightly  increase  the  required  adhesion,  but  the  effect  in  this  case 
is  very  slight,  about  one  pound  per  square  inch. 

Since  the  variation  of  j  is  very  little  for  the  usual  variations 
in  percentage  of  steel  and  quality  of  concrete,  it  is  a  common 
practice  to  consider  that,  as  applied  to  this  equation,  j  has  the 
uniform  value  of  .875,  or  |.  This  would  reduce  Equation  (13)  to 


which  means  that  v,  the  maximum  unit  horizontal  or  vertical 
shear  in  a  section,  is  about  ^  more  than  the  average  shear,  found 
by  dividing  the  total  shear  by  the  effective  section  of  the  beam. 
Vertical  Shear  and  Diagonal  Tension.  Beams  which  arc 
tested  to  destruction  frequently  fail  at  the  ends  long  before  the 
transverse  strength  at  the  center  has  been  fully  developed. 
Even  if  the  bond  between  the  steel  and  the  concrete  is  amply 
strong  for  the  requirements,  the  beam  may  fail  on  account  of  the 
shearing  or  diagonal  stresses  in  the  concrete  between  the  steel 
and  the  neutral  axis.  According  to  the  best  theory  on  the  sub- 


REINFORCED  CONCRETE  79 

ject,  supplemented  by  tests,  the  unit  diagonal  stress  may  amount 
to  double  the  unit  vertical  shear. 

Methods  of  Guarding  against  Failure  by  Shear  or  by 
Diagonal  Tension.  The  failure  of  a  beam  by  actual  shear  is 
almost  unknown.  The  failures  usually  ascribed  to  shear  are 
generally  caused  by  diagonal  tension.  A  solution  of  the  very 
simple  Equation  (13)  will  indicate  the  intensity  of  the  vertical 
shear.  If  a  beam  is  so  reinforced  that  it  will  safely  stand  the 
tests  for  moment,  diagonal  shear,  and  bond  adhesion,  there  is 
almost  no  question  of  its  ability  to  resist  vertical  shear. 

Resistance  to  Diagonal  Tension  by  Bending  Bars  or  by  Use 
of  Stirrups.  Resistance  to  diagonal  tension  is  furnished  by 
bending  up  the  main  reinforcing  bars,  and  also  by  the  use  of 
stirrups.  Unfortunately,  it  seems  impossible  to  devise  any  sim- 
ple, practicable  rules  (like  those  for  resisting  moment)  for  the 
precise  design  of  reinforcement  to  resist  diagonal  tension. 

Since  the  theory  is  so  uncertain,  an  empirical  method  has 
developed  which  practice  has  shown  to  be  safe  and  which  is, 
fortunately,  so  inexpensive  that  any  further  economies  are  of 
little  importance.  The  accepted  method  may  be  described  as 
follows:  First,  one  or  more  of  the  moment  bars  are  bent  up  at 
an  angle  of  30  degrees  to  45  degTees  near  each  end  of  the  beam, 
but  one  or  two  bars  are  always  allowed  to  run  straight  through. 
If  the  beam  is  very  short  and  there  are  numerous  bars,  the  bends 
are  made  at  various  distances  from  the  ends,  as  fast  as  the 
moment  bars  can  be  spared  from  their  primary  work  of  resisting 
moment.  Second,  vertical  •  stirrups  are  placed  throughout  the 
length  of  the  beam.  Near  the  ends  of  the  beam,  the  stirrups 
should  be  spaced  about  one-half  the  depth  of  the  beam.  At  the 
center  there  is  no  need  for  stirrups,  except  as  they  keep  the 
other  reinforcement  in  place  during  construction,  and  therefore 
the  spacing  is  gradually  widened  from  the  ends  toward  the 
center.  Third,  round  bars  are  preferable  to  square,  since  they 
bend  more  easily  into  the  exact  shape  desired.  The  size  should 
vary  in  general  accordance  with  the  size  of  the  beam  —  :}-inch, 
uj-inch,  and  f-inch  are  the  most  common  sizes,, but  -J-inch  bars 
might  be  used  for  heavy  deep  beams  of  short  span. 


80  REINFORCED  CONCRETE 

Calculations  by  Diagrams   of  Related   Factors.    A  very 

large  proportion  of  concrete  work  is  done  with  a  grade  of  con- 
crete such  that  we  may  call  the  ratio  n  of  the  moduli  of  the 
steel  and  the  concrete  either  12  or  15.  The  working  values  of  the 
stresses  in  the  steel  and  the  concrete,  s  and  c,  are  determined 
either  by  public  regulation  or  by  the  engineer's  estimate  of  the 
proper  values  to  be  used.  The  diagrams,  Figs.  20  and  21,  fully 
cover  the  whole  range  of  practicable  values  for  steel  and  for 
stone  concrete.  In  the  previous  problems  all  values  have  been 
calculated  on  the  basis  of  formulas.  By  means  of  these  dia- 
grams all  needed  values,  on  the  basis  of  the  other  factors,  may 
be  read  from  the  diagram  with  sufficient  accuracy  for  practical 
work.  In  addition,  the  diagrams  enable  one  to  note  readily  the 
effect  of  any  proposed  change  in  one  or  more  factors. 

Illustrative  Examples.  1.  If  a  beam,  made  of  concrete  such 
that  n  =  15,  is  to  be  so  loaded  that  when  the  stress  in  the  steel  s 
is  16,000,  the  stress  in  the  concrete  c  shall  simultaneously  be  600, 
the  steel  ratio  p  must  be  .00675.  This  is  found  on  the  diagram, 
Fig.  20,  for  n  =  15  by  following  the  line  s  =  16,000  to  its  inter- 
section with  the  line  c  =  600.  The  intersection  point,  measured 
on  the  steel  ratio  scale  at  the  bottom  of  the  diagram,  reads  .00675. 
Also,  running  horizontally  from  the  intersection  point  to  the 
scale  at  the  left,  we  read  R  =  95,  which  is  the  factor  for  bd2 
in  the  moment  equation,  Equation  (12).  Incidentally,  the  cor- 
responding values  of  k  and  j  for  this  steel  ratio  may  be  obtained, 
with  greater  convenience,  from  this  diagram,  although  they  are 
also  obtainable  from  the  more  general  diagram,  Fig.  17. 

2.  Assume  that,  for  reasons  discussed  on  page  60,  it  is  de- 
cided to  increase  the  steel  ratio  to  1.2  per  cent.  Following  the 
vertical  line  for  p  =  .012,  we  find  it  intersects  the  line  c  —  600 
at  a  point  where  R  =  114,  but  the  point  is  about  halfway  be- 
tween the  lines  s  =  10,000  and  s  =  12,000,  indicating  that,  using 
that  steel  ratio,  the  stress  in  the  steel  for  a  proper  stress  in  the 
concrete  is  far  less  than  the  usual  working  stress,  and  that  it 
would  be  about  11,000.  If  the  load  were  increased  so  that  s 
would  equal  16,000,  we  can  see  by  estimation  that  c  would  prob- 
ably be  over  800,  far  greater  than  a  proper  working  value. 


REINFORCED  CONCRETE 


81 


3.    Assume  p  =  .004,  c  =  600,  and  n  =  15.    How  much  then 
are  R  and  s*t    E  =  79  and  s  =  22,000,  which  is  impracticably 


STEEL  R/JTfO-p 
Fig,  20.  Curves  Showing  Values  of  Moment  Factor  R  for  n  « 15 


82 


REINFORCED  CONCRETE 


high.     The  diagram,  Fig.  21,  shows  plainly  that  for  low  steel 
ratios  the  values  of  s  are  abnormally  high  for  ordinary  values 

/6O 


RflTIO-p 

Fig.  21.   Curves  Showing  Values  of  Moment  Factor  R  for  n  =-=  12     ' 


REINFORCED  CONCRETE  83 

of  e;  on  the  other  hand,  for  high  steel  ratios,  the  ordinary  values 
of  c  cannot  utilize  the  full  working  strength  of  the  steel. 

Slabs  on  I-Beams.  The  skeleton  framework  of  buildings, 
especially  if  very  high,  is  frequently  made  of  steel,  even  when 
the  floors  have  concrete  girders,  beams,  and  slabs.  But  some- 
times even  the  girders  and  beams  are  made  of  steel  and  only  the 
slab  is  concrete ;  steel  I-beams  are  used  for  the  floor  girders  and 
beams,  and  the  beams  are  .connected  by  concrete  floor  slabs. 
Fig.  22.  These  are  usually  computed  on  the  basis  of  transverse 
beams  which  are  free  at  the  ends,  instead  of  considering  them 
as  continuous  beams,  which  will  add  about  50  per  cent  to  their 
strength.  Since  it  would  be  necessary  to  move  the  reinforcing 


LONGITUOfNflL  B/7/?5  TO  PREVENT 
5HRfNKfJGE  CROCKS 


EXPftHDED 
or  WIRE  L/TTH 


Fig.  22.    Diagram  Showing  Method  of  Placing  Concrete  Floor  Slabs  on 
J-^Beam  Girders 

steel  from  the  lower  part  to  the  upper  part  of  the  slab  when 
passing  over  the  floor  beams,  in  order  to  develop  the  additional 
strength  which  is  theoretically  possible  with  continuous  beams, 
and  since  this  is  not  usually  done,  it  is  by  far  the  safest  practice 
to  consider  all  floor  slabs  as  being  ''free-ended".  The  addi- 
tional strength  which  they*  undoubtedly  have  to  some  extent 
because  they  are  continuous  over  the  beams  merely  adds  indefi- 
nitely to  the  factor  of  safety.  Usually,  the  requirement  that  the 
I-beams  shall  be  fireproofed  by  surrounding  the  beam  itself 
with  a  layer  of  concrete  such  that  the  outer  surface  is  at  least 
2  inches  from  the  nearest  point  of  the  steel  beam  results  in  hav- 
ing a  shoulder  of  concrete  under  the  end  of  each  slab,  which 
materially  adds  to  its  structural  strength.  This  justifies  the  fre- 
quent practice  of  using  the  moment  formula  M  =  Wl  -+- 10, 
which  is  a  compromise  between  Wl  ~5-  8  and  Wl  -*- 12.  Even 


84 


REINFORCED  CONCRETE 


this  should  be  done  only  when  the  bars  are  run  into  the  adjoin- 
ing span  far  enough  so  that  the  bond  adhesion,  computed  at  a 
safe  working  value,  will  not  exceed  the  tension  in  the  steel,  and 
also  when  the  steel  is  raised  to  a  point  near  the  top  of  the  slab 
over  the  supports.  The  fireproofing  around  the  beam  must 
usually  be  kept  in  place  by  wrapping  a  small  sheet  of  expanded 
metal  or  wire  lath  around  the  lower  part  of  the  beam  before 
the  concrete  is  placed. 

Slabs  Reinforced  in  Both  Directions.  When  the  floor 
beams  are  spaced  nearly  equally  in  both  directions,  so  that  they 
form,  between  the  beams,  panels  which  are  nearly  square,  a 
considerable  saving  can  be  made  in  the  thickness  of  the  slab  by 
reinforcing  it  with  bars  running  in  both  directions.  The  the- 
oretical computation  of  the  strength  of  such  slabs  is  exceedingly 
complicated.  The  usual  method  is  to  estimate  that  the  total  load 
is  divided  into  two  parts  such  that  if  I  equals  the  length  of  a 
rectangular  panel  and  b  equals  the  breadth  (I  being  greater  than, 
or  equal  to  b),  then  the  ratio  of  the  load  carried  by  the  "[>" 
bars  is  given  by  the  proportion  Z4  -*-  (Z4  +  b4).  If  the  value  of 
this  proportion  is  worked  out  for  several  values  of  the  ratio 
/:  b,  we  have  the  percentages  which  are  given  by  the  tabular 
form  below: 


RATIO  I  :  b 

1.0 

1.1 

1.2 

1.3 

1.4 

1.5 

Proportion     of 
load    carried 

50% 

59% 

67% 

74% 

80% 

83% 

by  "b"  bars 

When  Z  and  b  are  equal,  each  set  of  bars  takes  half  the  load. 
When  I  is  only  50  per  cent  greater  than  I),  the  shorter  bars  take 
83  per  cent  of  the  load  and  it  is  uneconomical  to  use  bars  for 
transverse  moment  in  the  longer  direction.  The  lack  of  economy 
begins  at  about  25  per  cent  excess  length,  and  therefore  panels 
in  which  the  proportion  of  length  to  breadth  is  greater  than  125 
per  cent  should  be  reinforced  in  the  shorter  direction  only. 
Strictly  speaking,  the  slab  should  be  thicker  by  the  thickness  of 
one  set  of  reinforcing  bars. 


REINFORCED  CONCRETE  85 

Reinforcement  against  Temperature  Cracks.  The  modulus 
of  elasticity  of  ordinary  concrete  is  approximately  2,400,000 
pounds  per  square  inch,  while  its  ultimate  tensional  strength  is 
about  200  pounds  per  square  inch.  Therefore  a  pull  of  about 
-j-yj-fl^jof  the  length  would  nearly,  if  not  quite,  rupture  the  con- 
crete. The  coefficient  of  expansion  of  concrete  has  been  found 
to  be  almost  identical  with  that  of  steel,  or  .0000065  for  each 
degree  Fahrenheit.  Therefore,  if  a  block  of  concrete  were  held 
at  the  ends  with  absolute  rigidity,  while  its  temperature  was 
lowered  about  12  degrees,  the  stress  developed  in  the  concrete 
would  be  very  nearly,  if  not  quite,  at  the  rupture  point.  For- 
tunately, the  ends  will  not  usually  be  held  with  such  rigidity; 
but,  nevertheless,  it  does  generally  happen  that,  unless  the  entire 
mass  of  concrete  is  permitted  to  expand  and  contract  freely  so 
that  the  temperature  stresses  are  small,  the  stresses  will  usually 
localize  themselves  at  the  weak  point  of  the  cross  section,  wher- 
ever that  may  be,  and  will  there  develop  a  crack,  provided  the 
concrete  is  not  reinforced  with  "steel.  If,  however,  steel  is  well 
distributed  throughout  the  cross  section  of  the  concrete,  it  will 
prevent  the  concentration  of  the  stresses  at  local  points,  and  will 
distribute  it  uniformly  throughout  the  mass. 

Reinforced  concrete  structures  are  usually  provided  with  bars 
running  in  all  directions,  so  that  temperature  cracks  are  pre- 
vented, and  it  is  generally  unnecessary  to  make  any  special  pro- 
vision against  them.  The  most  common  exception  occurs  in  floor 
slabs,  which  structurally  require  bars  in  only  one  direction.  It 
is  found  that  cracks  parallel  with  the  bars  which  reinforce  the 
slab  will  be  prevented,  if  a  few  bars  are  laid  perpendicularly 
to  the  direction  of  the  main  reinforcing  bars.  Usually,  i-inch 
or  §-inch  bars,  spaced  about  2  feet  apart,  will  be  sufficient. 

Retaining  walls,  the  balustrades  of  bridges,  and  other  similar 
structures,  which  may  not  need  any  bars  for  purely  structural 
reasons,  should  be  provided  with  them  in  order  to  prevent  tem- 
perature cracks.  A  theoretical  determination  of  the  amount  of 
such  reinforcing  steel  is  practically  impossible,  since  it  depends 
on  assumptions  which  are  themselves  very  doubtful.  It  is 
usually  conceded  that  if  there  is  placed  in  the  concrete  an 


86  REINFORCED  CONCRETE 

amount  of  steel  whose  cross-sectional  area  equals  about  3  of  1 
per  cent  of  the  area  of  the  concrete,  the  structure  will  be  proof 
against  such  cracks.  Fortunately,  this  amount  of  steel  is  so 
small  that  any  great  refinement  in  its  determination  is  of  little 
importance.  Moreover,  since  such  bars  have  a  value  in  tying 
the  structure  together,  and  thus  add  somewhat  to  its  strength 
and  ability  to  resist  disintegration  due  to  vibrations,  the  bars 
are  usually  worth  what  they  cost. 

T=BEAM  CONSTRUCTION 

When  concrete  beams  are  laid  in  conjunction  with  overlying 
floor  slabs,  the  concrete  for  both  the  beams  and  the  slabs  being 
laid  in  one  operation,  the  strength  of  such  beams  is  very  much 

greater  than  their  strength  con- 
sidered merely  as  plain  beams, 
even  though  we  compute  the 
depth  of  the  beam  as  equal  to 
the  total  depth  from  the  bottom 
of  the  beam  to  the  top  of  the 
slab.  An  explanation  of  this 
added  strength  may  be  made  as 
follows : 

If  we  construct  a  very  wide 

Fig.  23.    Diagram  of  T-Beam       beam  as  shown  by  the  complete 
in  Cross  Section  ,     .     -,-..       <-.„    ., 

rectangle  in  Fig.  23,  there  is  no 

hesitation  about  calculating  its  strength  as  that  of  a  plain  beam 
whose  width  is  ~b,  and  whose  effective  depth  to  the  reinforcement 
is  d.  Our  previous  study  in  plain  beams  has  shown  us  that  the 
steel  in  the  bottom  of  the  beam  takes  care  of  practically  all  the 
tension ;  that  the  neutral  axis  of  the  beam  is  somewhat  above  the 
center  of  its  height ;  that  the  only  work  of  the  concrete  below  the 
neutral  axis  is  to  transfer  the  stress  in  the  steel  to  the  concrete 
in  the  top  of  the  beam ;  and  that  even  in  this  work  it  must  be 
assisted  somewhat  by  stirrups  or  by  bending  up  the  steel  bars. 
If,  therefore,  we  cut  out  from  the  lower  corners  of  the  beam  two 
rectangles,  as  shown  by  the  unshaded  areas,  we  are  saving  a 
very  large  part  of  the  concrete,  with  very  little  loss  in  the 


REINFORCED  CONCRETE 


87 


strength  of  the  beam,  provided  we  can  fulfil  certain  conditions. 
The  steel,  instead  of  being  distributed  uniformly  throughout 
the  bottom  of  the  wide  beam,  is  concentrated  into  the  compara- 
tively narrow  portion  which  we  shall  hereafter  call  the  rib  of 
the  beam.  The  concentrated  tension  in  the  bottom  of  this  rib 
must  be  transferred  to  the  compression  area  at  the  top  of  the 
beam.  We  must  also  design  the  beam  so  that  the  shearing 
stresses  in  the  plane  mn  immediately  below  the  slab  shall  not 
exceed  the  allowable  shearing  stress  in  the  concrete.  We  must 
also  provide  that  failure  shall  not  occur  on  account  of  shearing 
in  the  vertical  planes  mr  and  ns  between  the  sides  of  the  beam 
and  the  flanges. 

Resisting  Moments  of  T-Beams.     The  resisting  moments  of 
T-beams  will  be  computed  in  accordance  with  straight-line  for- 

b'- 


r^T 


•///^  N£UTf?fJL  f?X/5 


Fig.  24.   Compression  Stress  Diagram  for  T-Beam 

mulas.  There  are  three  possible  cases,  according  as  the  neutral 
axis  is:  (1)  below  the  bottom  of  the  slab  (which  is  the  most 
common  case,  and  which  is  illustrated  in  Fig.  24)  ;  (2)  at  the 
bottom  of  the  slab;  or  (3)  above  it.  All  possible  effect  of  ten- 
sion in  the  concrete  is  ignored.  For  Case  I,  even  the  compres- 
sion furnished  by  the  concrete  between  the  neutral  axis  and 
the  under  side  of  the  slab  is  ignored.  Such  compression  is,  of 
course,  zero  at  the  neutral  axis;  its  maximum  value  at  the 
bottom  of  the  slab  is  small;  the  summation  of  its  compression 
is  evidently  small;  the  lever  arm  is  certainly  not  more  than 
§  y;  therefore,  the  moment  due  to  such  compression  is  insignifi- 
cant compared  with  the  resisting  moment  due  to  the  slab.  The 
computations  are  much  more  complicated  if  it  is  included; 


88  REINFORCED  CONCRETE 

without  it  the  resulting  error  is  a  very  small  percentage  of  the 
true  figure,  and  the  error  is  on  the  side  of  safety. 

Case  I.     If  c  is  the  maximum  compression  at  the  top  of  the 
slab,  and  the  stress-strain  diagram  is  rectilinear,  as  in  Fig.  24, 

then  the  compression  at  the  bottom  of  the  slab  is  c       ~  t 

faT 
The  average  compression  equals 

i      /  I  rCCi  I  .  C        /it 


The  total  compression  C  equals  the  average  compression  multi- 
plied by  the  area  b't;  or 

r  .  ~\ 

(14) 

The  center  of  gravity  of  the  compressive  stresses  is  evidently 
at  the  center  of  gravity  of  the  trapezoid  of  pressures.  The 
distance  x  of  this  center  of  gravity  from  the  top  of  the  beam 
is  given  by  the  formula 

=  t  y3kd  —  2t 
3       2kd  —  t 

It  has  already  been  shown  that 

es  CM  _        kd 

€C       s         d~kd 


Combining  this  equation  with  Equation  (14),  we  may  eliminate 

And  +  \  b't* 
An  +  b't 


—  ,  and  obtain  a  value 


If  the  percentage  of  steel  is  chosen  at  random,  the  beam  will 
probably  be  over-reinforced  or  under-reinforced.  In  general, 
it  will  therefore  be  necessary  to  compute  the  moment  with 
reference  to  the  steel  and  also  with  reference  to  the  concrete, 
and,  as  before  with  plain  beams,  Equation  (12),  we  shall  have  a 
pair  of  equations 


REINFORCED  CONCRETE  89 

-   /   f  JL       —  i      1  '    - 

M8  =  As  (d  —  x)=  pb'ds  (d  —  x) 

Case  II.  If  we  place  kd  =  t  in  the  equation  just  above 
Equation  (16),  and  solve  for  d,  we  have  a  relation  between 
d,  c,  s}  n,  and  t,  which  holds  when  the  neutral  axis  is  just  at 
the  bottom  of  the  slab.  The  equation  becomes 


A  combination  of  dimensions  and  stresses  which  would  place 
the  neutral  axis  exactly  in  this  position  is  improbable,  although 
readily  possible;  but  Equation  (18)  is  very  useful  in  deter- 
mining whether  a  given  numerical  problem  belongs  to  Case  I 
or  Case  III.  When  the  stresses  s  and  c  in  the  steel  and  con- 
crete, the  ratio  n  of  the  elasticities,  and  the  thickness  t  of  the 
slab  are  all  determined,  then  the  solution  of  Equation  (18) 
will  give  a  value  of  d  which  would  bring  the  neutral  axis  at  the 
bottom  of  the  slab.  But  it  should  not  be  forgotten  that  the 
compression  in  the  concrete  c  and  the  tension  in  the  steel  s 
will  not  simultaneously  have  certain  definite  values— say 
c  =  500,  and  s  =  16,000— Unless  the  percentage  of  steel  has 
been  so  chosen  as  to  give  those  simultaneous  values.  When,  as 
is  usual,  some  other  percentage  of  steel  is  used,  the  equation 
is  not  strictly  applicable,  and  it  therefore  should  not  be  used 
to  determine  a  value  of  d  which  will  place  the  neutral  axis  at 
the  bottom  of  the  slab  and  thus  simplify  somewhat  the  nu- 
merical calculations.  For  example,  for  c  =  500,  s  =  16,000, 
n  =  12,  and  t  =  4  inches,  d  will  equal  14.67  inches.  Of  course 
this  particular  depth  may  not  satisfy  the  requirements  of  the 
problem.  If  the  proper  value  for  d  is  less  than  that  indicated 
by  Equation  (18),  the  problem  belongs  to  Case  III;  if  it  is 
more,  the  problem  belongs  to  Case  I. 

Case  111.  The  diagram  of  pressure  is  very  similar  to  that 
in  Fig.  24,  except  that  it  is  a  triangle  instead  of  a  trapezoid, 
the  triangle  having  a  base  c  and  a  height  kd  which  is  less  than  t. 
The  center  of  compression  is  at  one-third  the  height  from  the 
base,  or  x  =  J  kd.  Equations  (9)  to  (12)  are  applicable  to  this 


90  REINFORCED  CONCRETE 

case  as  well  as  to  Case  II,  which  may  be  considered  merely  as 
the  limiting  case  to  Case  III.  But  it  should  be  remembered 
that  b'  refers  to  the  width  of  the  flange  or  slab,  and  not  to  the 
width  of  the  stem  or  rib. 

Width  of  Flange.  The  width  V  of  the  flange  is  usually 
considered  as  equal  to  the  width  between  adjacent  beams,  or  as 
extending  from  the  middle  of  one  panel  to  the  middle  of  the 
next.  The  chief  danger  in  such  an  assumption  lies  in  the  fact 
that  if  the  beams  are  very  far  apart,  they  must  have  corre- 
sponding strength  to  carry  such  a  floor  load,  and  the  shearing 
stresses  between  the  rib  and  the  slab  will  be  very  great.  (The 
method  of  calculating  such  shear  will  be  given  later.)  It  some- 
times happens  (as  illustrated  on  page  100),  that  the  width  of 
slab  on  each  side  of  the  rib  is  almost  indefinite.  In  such  a  case 
we  must  arbitrarily  assume  some  limit.  Since  the  unit  shear 
is  greater  for  short  beams  than  for  long  beams,  the  slab  thick- 
ness should  bear  some  relation  to  the  span  of  the  beam.  The 
building  code  specifications  for  New  York  City  specify  that 
the  width  on  each  side  of  the  beam  shall  not  be  greater  than 
one-sixth  of  the  beam  span,  and  not  greater  than  six  times  the 
slab  thickness.  If  the  width  of  the  rib  is  twice  the  slab  thick- 
ness, this  rule  permits  the  width  of  flange  &'  to  be  fourteen 
times  the  slab  thickness,  and  something  over  one-third  of  the 
beam  span,  whichever  is  the  less.  If  the  compression  is  com- 
puted for  two  cases,  both  of  which  have  the  same  size  of  rib, 
the  same  steel,  and  the  same  thickness  of  slab,  but  different 
slab  widths,  it  is  found,  as  might  be  expected,  that  for  the 
narrower  slab  width  the  unit  compression  is  greater,  the  neutral 
axis  is  very  slightly  lower,  and  even  the  unit  tension  in  the 
steel  is  slightly  greater.  No  demonstration  has  ever  been  made 
to  determine  any  limitation  of  width  of  slab  beyond  which,  no 
compression  would  be  developed  by  the  transverse  stress  in  a 
T-beam  rib  under  it.  It  is  probably  safe  to  assume  that  com- 
pression extends  for  six  times  the  thickness  of  the  slab  on  each 
side  of  the  rib.  If  the  beam  as  a  whole  is  safe  on  this  basis, 
then  it  is  still  safer  for  any  additional  width  to  which  the 
compression  may  extend. 


REINFORCED  CONCRETE  91 

Width  of  Rib.  Since  it  is  assumed  that  all  of  the  com- 
pression occurs  in  the  slab,  the  only  work  done  by  the  concrete 
in  the  rib  is  to  transfer  the  tension  in  the  steel  to  the  slab,  to 
resist  the  shearing  and  web  stresses,  and  to  keep  the  bars  in 
their  proper  places.  The  width  of  the  rib  is  to  a  certain  extent 
determined  by  the  amount  of  reinforcing-  steel  which  must  be 
placed  in  the  rib,  and  by  the  number  of  bars — whether  it  is 
desirable  to  use  two  or  more  rows  of  bars  instead  of  merely 
one  row.  As  indicated  in  Fig.  23,  the  amount  of  steel  required 
in  the  base  of  a  T-beam  is  frequently  so  great  that  two  rows 
of  bars  are  necessary  in  order  that  the  bars  may  have  a  suffi- 
cient spacing  between  them  so  that  the  concrete  between  will 
not  split  apart.  Although  it  would  be  difficult  to  develop  any 
rule  for  the  proper  spacing  between  bars  without  making 
assumptions  which  are  perhaps  doubtful,  the  following  empir- 
ical rule  is  frequently  adopted  by  designers:  The  minimum 
spacing  between  bars,  center  to  center,  should  be  two  and  one- 
quarter  times  the  diameter  of  the  bars.  Fire  insurance  and 
municipal  specifications  usually  require  that  there  shall  be  one 
and  one-half  to  two  inches  clear  outside  of  the  steel.  This 
means  that  the  beam  shall  be  three  or  four  inches  wider  than 
the  net  width  from  out  to  out  of  the  extreme  bars.  The  data 
given  in  Table  XVIII  will  therefore  be  found  very  convenient, 
since,  when  a  certain  number  of  bars  of  given  size  are  to  be 
used,  a  glance  at  the  table  will  show  immediately  whether  it  is 
possible  to  space  them  in  one  row ;  and,  if  it  is  not  possible,  the 
necessary  arrangement  can  be  very  readily  designed.  For  exam- 
ple, assume  that  six  f-inch  bars  are  to  be  used  in  a  beam.  The 
table  shows  immediately  that,  according  to  the  rule,  the  required 
width  of  the  beam  will  be  14.72  inches ;  but  if,  for  any  reason, 
a  beam  11  inches  wide  is  considered  preferable,  the  table  shows 
that  four  f-inch  bars  may  be  placed  side  by  side,  leaving  two 
bars  to  be  placed  in  an  upper  row.  According  to  the  same 
rule  regarding  the  spacing  of  the  bars  in  vertical  rows,  the 
distance  from  center  to  center  of  the  two  rows  should  be 
2.25  X  .875  =  1.97  inches ;  that  is,  the  rows  should  be,  say, 
2  inches  apart,  center  to  center.  It  should  also  be  noted  that  the 


92 


REINFORCED  CONCRETE 


TABLE  XVIII 

Required    Width   of    Beam,   Allowing   2\  X  d,  for  Spacing, 
Center  to  Center,  and  2  Inches  Clear  on  Each  Side 


Formula 


n  —  Dumber  of  bars  ;  d  =  diameter 
Width  =  (n  —  1)  2.23  d  +  d  +  4  =  2.25  nd  —  1.25  d  +  4 


No. 

DIAMETER  OF  BARS 

OF 

BARS 

JIN. 

UN. 

UN. 

UN. 

1  IN. 

11  IN. 

11  IN. 

2 

5.62 

6.03 

6.44 

6.84 

7.25 

7.66 

8.06 

3 

6.75 

7.44 

8.13 

8.81 

9.50 

8.19 

10.87 

4 

7.87 

8.84 

9.81 

10.78 

11.75 

12.72 

13.68 

5 

9.00 

10.25 

11.50 

12.75 

14.00 

15.25 

16.50 

6 

10.12 

11.65 

13.19 

14.72 

16.25 

17.78 

19.31 

7 

11.25 

13.06 

14.87 

16.68 

18.50 

20.31 

22.12 

8 

12.37 

14.46 

16.56 

18.65 

20.75 

22.84 

24.94 

9 

13.50 

15.87 

18.25 

20.62 

23.00 

25.37 

27.75 

10 

14.62 

17.28 

19.94 

22.59 

25.25 

27.90 

30.56 

NOTE. — For  side  protection  of  only  one  and  one-half  inches,  deduct 
one  inch  from  above  figures. 

plane  of  the  center  of  gravity  of  this  steel  is  at  two-fifths  of  the 
distance  between  the  bars  above  the  lower  row,  or  that  it  is  .8 
inch  above  the  center  of  the  lower  row. 

Examples.  1.  Assume  that  a  5-inch  slab  is  supporting  a  load  on 
beams  spaced  5  feet  apart,  the  beams  having  a  span  of  20  feet.  Assume 
that  the  moment  of  the  beam  has  been  computed  as  900,000  inch-pounds. 
What  will  be  the  dimensions  of  the  beam  if  the  concrete  is  not  to  have 
a  compression  greater  than  600  pounds  per  square  inch  and  the  tension 
of  the  steel  is  not  to  be  greater  than  16,000  pounds  per  square  inch? 

Solution.  There  are  an  indefinite  number  of  solutions  to  this  prob- 
lem. There  are  several  terms  in  Equation  (17)  which  are  mutually 
dependent ;  it  is,  therefore,  impracticable  to  obtain  directly  the 
depth  of  the  beam  on  the  basis  of  assuming  the  other  quantities ; 
therefore,  it  is  only  possible  to  assume  figures  which  experience  shows 
will  give  approximately  accurate  results,  and  then  to  test  these  figures 
to  see  whether  all  the  conditions  are  satisfied.  Within  limitations,  we 
may  assume  the  amount  of  steel  to  be  used,  and  determine  the  depth 
of  beam  which  will  satisfy  the  other  conditions,  together  with  that  of 
the  assumed  area  of  steel.  For  example,  we  shall  assume  that  six 
2-inch  square  bars  having  an  area  of  4.59  square  inches  will  be  a  suit- 
able reinforcement  for  this  beam.  We  shall  also  assume  as  a  trial 
figure  that  x  equals  1.5.  Substituting  these  values  in  the  second  for- 
mula of  Equation  (17)  we  may  write  that  formula 

900,000  =  4.59  X  16,000 (d  —  1.5) 

Solving  for  d,  we  find  that  d  =  13.75  inches.  If  we  test  this  value  by 
means  of  Equation  (18)  we  shall'  find  that,  substituting  the  values  of 


REINFORCED  CONCRETE  93 

/,  c,  n,  and  s  in  Equation  (18),  the  resulting  value  of  d  =  16.11  inches. 
This  shows  that  if  we  make  the  depth  of  the  beam  only  13.75,  the 
neutral  axis  will  be  within  the  slab,  and  the  problem  cornes  under 
Case  III,  to  which  we  must  apply  Equation  (12).  Dividing  the  area 
of  the  steel,  4.59,  by  (fc'Xd),  we  have  the  value  of  p  =  .00556.  Inter- 
polating with  this  value  of  p  in  Table  XI,  we  find  that  when  n  =  l2, 
then  £  =  .303:  fcd  =  4.17;  x  --=  1.39  ;  and  yd  =  12. 36.  Substituting  these 
values  in  Equation  (12),  we  find  that  the  moment  900,000  ~  1.545  c, 
or  that  c  =  582  pounds  per  square  inch.  This  shows  that  the  unit  com- 
pression of  the  concrete  is  safely  within  the  required  figure.  Substituting 
the  known  values  in  the  second  part  of  Equation  (12)  we  find  that  the 
stress  in  the  steel  s  equals  about  15,860  pounds  per  square  inch. 

2.  Assume  that  a  floor  is  loaded  so  that  the  total  weight  of  live  and 
dead  load  is  200  pounds  per  square  foot ;  assume  that  the  T-beams  are  to 
be  5  feet  apart,  and  that  the  slab  is  to  be  4  inches  thick  ;  assume  that  the 
span  of  the  T-beams  is  30  feet.  Find  the  dimensions  of  the  beams. 

Solution.  We  have  in  the  ease  of  this  floor  an  area  of  150  square 
feet  to  be  supported  by  each  beam,  which  will  give  a  total  load  of  30,000 
pounds  on  each  beam.  The  moment  at  the  center  of  such  a  beam  will 
therefore  be  equal  to  the  total  load,  multiplied  by  one-eighth  of  the  span 
(expressed  in  inches),  and  the  moment  is  therefore  1,350,000  inch- 
pounds.  As  a  trial  value,  we  shall  assume  that  the  beam  is  to  be 
reinforced  with  six  |-inch  square  bars,  which  have  an  area  of  3.375 
square  inches.  Substituting  this  value  of  the  area  in  the  second  part 
of  Equation  (17),  and  assuming  that  s  equals  16,000  pounds  per  square 
inch,  we  find  that  the  approximate  value  for  (d  —  #)  is  25  inches. 
This  is  very  much  greater  than  the  value  of  d  that  would  be  found 
from  substituting  the  proper  values  in  Equation  (18),  so  that  we  know 
at  once  that  the  problem  must  be  solved  by  the  methods  of  Case  I. 
For  a  4-inch  slab,  the  value  of  x  must  be  somewhere  between  1.33 
and  2.0.  As  a  trial  value,  we  may  call  it  1.5,  and  this  means  that  d 
will  equal  26.5  inches.  Assuming  that  this  slab  is  to  be  made  of  con- 
crete using  a  value  for  n  equal  to  12,  we  know  all  the  values  in  Equa- 
tion (16),  and  may  solve  for  A'd,,  which  we  find  equals  5.54  inches.  As 
a  check  on  the  approximations  made  above,  we  may  substitute  this 
value  of  kd,  and  also  the  value  of  t  in  Equation  (15),  and  obtain  a 
more  precise  value  of  x,  which  we  find  equals  1.62.  Substituting  the 
value  of  the  moment  and  the  other  known  quantities  in  the  upper  for- 
mula of  Equation  (17),  we  may  solve  for  the  value  of  c,  and  obtain 
the  value  that  c  equals  352  pounds  per  square  inch.  This  value  for  c 
is  so  very  moderate  that  it  would  probably  be  economy  to  assume  a 
lower  value  for  the  area  of  the  steel,  and  increase  the  unit  compression 
in  the  concrete  ;  but  this  solution  will  not  be  here  worked  out. 

Shearing  Stresses  between  Beam  and  Slab.  Every  solution 
for  T-beam  construction  should  be  tested  at  least  to  the  extent 
of  knowing  that  there  is  no  danger  of  failure  on  account  of  the 
shear  between  the  beam  and  the  slab,  either  on  the  horizontal 
plane  at  the  lower  edge  of  the  slab,  or  in  the  two  vertical  planes 


94  REINFORCED  CONCRETE 

along  the  two  sides  of  the  beam.  Let  us  consider  a  'T-beam 
such  as  is  illustrated  in  Fig.  25.  In  the  lower  part  of  the  figure 
is  represented  one-half  of  the  length  of  the  flange,  which  is  con- 
sidered as  separated  from  the  rib.  Following  the  usual  method 
of  regarding  this  as  a  free  body  in  space,  acted  on  by  external 
forces  and  by  such  internal  forces  as  are  necessary  to  "produce 
equilibrium,  we  find  that  it  is  acted  on  at  the  left  end  by  the 
abutment  reaction,  which  is  a  vertical  force,  and  also  by  a 
vertical  load  on  top.  We  may  consider  Pf  as  representing  the 
summation  of  all  compressive  forces  acting  on  the  flanges  at 
the  center  of  the  beam.  In  order  to  produce  equilibrium,  there 
must  be  a  shearing  force  acting  on  the  under  side  of  the  flange. 


iumuuuuml 


Fig.  25.   Diagram  Showing  Analysis  of  Stresses  in  T-Beam 

We  represent  this  force  by  Sh.  Since  these  two  forces  are  the 
only  horizontal  forces,  or  forces  with  horizontal  components, 
which  are  acting  on  this  free  body  in  space,  P'  must  equal  S^. 
Let  us  consider  z  as  representing  the  shearing  force  per  unit  of 
area.  We  know  from  the  laws  of  mechanics,  that,  with  a  uni- 
formly distributed  load  on  the  beam,  the  shearing  force  is  maxi- 
mum at  the  ends  of  the  beam,  and  diminishes  uniformly  toward 
the  center,  where  it  is  zero.  Therefore  the  average  value  of  the 
unit  shear  for  the  half-length  of  the  beam,  must  equal  \  z.  As 
before,  we  represent  the  width  of  the  rib  by  b.  For  convenience 
in  future  computations,  we  shall  consider  L  as  representing  the 
length  of  the  beam,  measured  in  feet.  All  other  dimensions  are 
measured  in  inches.  Therefore  the  total  shearing  force  along 
the  lower  side  of  the  flange,  will  be 

Sh  =  laXbXlLX12  =  3bzL  (19) 


REINFORCED  CONCRETE  95 

There  is  also  a  possibility  that  a  beam  may  fail  in  case  the 
flange,  or  the  slab,  is  too  thin ;  but  the  slab  is  always  reinforced 
by  bars  which  are  transverse  to  the  beam,  and  the  slab  will  be 
placed  on  both  sides  of  the  beam,  giving  two  shearing  surfaces. 

Illustrative  Example.  It  is  required  to  test  the  beam  which 
was  computed  in  Example  1  on  page  92.  Here  the  total  compres- 
sive  stress  in  the  flange  equals  i  cb'kd  =  -|  X  582  X  60  X  4.17 
—  72,808  pounds.  But  this  compressive  stress  measures  the 
shearing  stress  Sh  between  the  flange  and  the  rib.  This  beam 
requires  six  f -inch  bars  for  the  reinforcement.  We  shall  assume 
that  the  rib  is  to  be  11  inches  wide,  that  four  of  the  bars  are 
placed  in  the  bottom  row,  and  two  bars  about  2  inches  above 
them.  The  effect  of  this  will  be  to  deepen  the  beam  slightly, 
since  d  measures  the  depth  of  the  beam  to  the  center  of  the  rein- 
forcement, and,  as  already  computed  numerically  on  page  91, 
the  center  of  gravity  of  this  combination  will  be  .8  of  an  inch 
above  the  center  of  gravity  of  the  lower  row  of  bars.  Substi- 
tuting in  Equation  (19)  the  values  ^  =  72,808,  b  =  11,  and 
L  =  20,  we  find  for  the  unit-value  of  z,  110  pounds  per  square 
inch.  This  shows  that  the  assumed  dimensions  of  the  beam  are 
satisfactory  in  this  respect,  since  the  true  shearing  stress  per- 
missible in  concrete  is  higher  than  this. 

But  the  beam  must  be  tested  also  for  its  ability  to  withstand 
shear  in  vertical  planes  along  the  sides  of  the  rib.  Since  the 
slab  in  this  case  is  5  inches  thick  and  we  can  count  on  both 
surfaces  to  withstand  the  shear,  we  have  a  width  of  10  inches 
to  withstand  the  shear,  as  compared  with  the  11  inches  on  the 
underside  of  the  slab.  The  unit  shear  would  therefore  be  irr 
of  the  unit  shear  on  the  underside  of  the  slab,  and  would  equal 
121  pounds  per  square  inch.  This  is  at  or  beyond  the  limit, 
120,  but  danger  of  failure  in  this  respect  is  avoided  by  the 
fact  that  the  slab  contains  bars  which  are  inserted  to  reinforce 
it,  and  which  have  such  an  area  that  they  will  effectively  prevent 
any  shearing  in  this  way. 

Testing  Example  2  similarly,  we  may  find  the  total  com- 
pression C  from  Equation  (14),  which  here  equals  As  = 
3.375  X  16,000  =  54,000  pounds.  The  steel  reinforcement  is 


96  REINFORCED  CONCRETE 

six  f-inch  bars,  and,  from  Table  XVIII,  if  the  bars  are  placed 
side  by  side,  the  beam  must  be  13.19  inches  in  width,  or,  in  round 
numbers,  13|  inches.  Sh  =  54,000,  6  =  13.25,  L  =  30;  there- 
fore, from  Equation  (19),  2  =  45  pounds  per  square  inch. 
Such  a  value  is  of  course  perfectly  safe.  The  shear  along  the 
sides  of  the  beam  will  be  considerably  greater,  since  the  slab  IF 
only  4  inches  thick,  and  twice  the  thickness  is  but  8  inches; 
therefore,  the  maximum  unit  shear  along  the  sides  will  equal  45 
times  the  ratio  of  13.25  to  8,  or  75  pounds  per  square  inch. 
Even  this  would  be  perfectly  safe,  to  say  nothing  of  the  addi- 
tional shearing  strength  afforded  by  the  slab  bars. 

Shear  in  a  T-Beam.  The  shear  here  referred  to  is  the  shear 
of  the  beam  as  a  whole  on"  any  vertical  section.  It  does  not 
refer  to  the  shearing  stresses  between  the  slab  and  the  rib. 

The  theoretical  computation  of  the  shear  of  a  T-beam  is  a 
very  complicated  problem.  Fortunately,  it  is  unnecessary  to 
attempt  to  solve  it  exactly.  The  shearing  resistance  is  certainly 
far  greater  in  the  case  of  a  T-beam  than  in  the  case  of  a  plain 
beam  of  the  same  width  and  total  depth  and  loaded  with  the 
same  total  load.  Therefore,  if  the  shearing  strength  is  suffi- 
cient, according  to  the  rule,  for  a  plain  beam,  it  is  certainly 
sufficient  for  the  T-beam.  In  Example  1,  above  cited,  the  total 
load  on  the  beam  is  30,000  pounds.  Therefore  the  maximum 
shear  V  at  the  end  of  the  beam  is  15,000  pounds.  In  this  par- 
ticular case,  jd  =  12.36.  For  this  beam,  d  =  13.75  inches,  and 
b  =  11  inches.  Substituting  these  values  in  Equation  (13),  we 

15,000 

=  ai  x  12.36  =  113  lb' per  sq" m- 

Although  this  is  probably  a  very  safe  stress  for  direct  shearing, 
it  is  more  than  double  the  allowable  direct  tension,  40,  due  to 
the  diagonal  stresses;  and  therefore  ample  reinforcement  must 
be  provided.  If  only  two  of  the  5-inch  bars  are  turned  at  an 
angle  of  45  degrees  at  the  end,  these  two  bars  will  have  an  area 
of  1.54  square  inches,  and  will  have  a  working  tensile  strength 
(at  the  unit  stress  of  16,000  pounds)  of  24,640  pounds.  This 
is  more  than  the  total  vertical  shear  at  the  ends  of  the  beam, 


REINFORCED  CONCRETE 


97 


and  a  pair  of  turned-up  bars  would  therefore  take  care  of  the 
shear  at  that  point.  But  considering  that  stirrups  would  be 
used  on  a  beam  of  20-foot  span,  it  will  be  very  easy  to  design 
these  stirrups  to  provide  for  this  shear,  as  was  explained  on 
a  previous  page. 

Illustration  of  Slab,  Beam,  and  Girder  Construction.  As- 
sume a  floor  construction  as  outlined  in  skeleton  form  in  Fig.  26. 
The  columns  are  spaced  16  feet  by  20  feet.  Girders  which  sup- 
port the  alternate  rows  of  beams  connect  the  columns  in  the 
16-foot  direction.  The  live  load  on  the  floor  is  150  pounds  per 
square  foot.  The  con- 
crete is  to  be  a  1:2:4 
mixture,  with  n  =  12 
and  c  =  600.  Required 
the  proper  dimensions 
for  the  slab,  beams,  and 
girders. 

Slab.  The  load  on  the 
girders  may  be  computed 
in  either  one  of  two 
ways,  both  of  which  give 
the  same  results.  We 
must  consider  that  each 
beam  supports  an  area  of  8  feet  by  20  feet.  We  may  there- 
fore consider  that  girder  d  supports  the  load  of  b  (on  a 
floor  area  8  feet  by  20  feet)  as  a  concentrated  load  in  the 
center.  Or,  ignoring  the  beams,  we  may  consider  that  the 
girder  supports  a  uniformly  distributed  load  on  an  area  16  feet 
by  20  feet.  The  moment  in  either  case  is  the  same.  Assume 
that  we  shall  use  a  1  per  cent  reinforcement  in  the  slab.  Then, 
from  Table  XII,  with  n  =  12,  and  p  =  .01,  we  find  that 
k  =  .385 ;  then  x  =  .128  d,  or  jd  =  .872  d.  As  a  trial,  we  esti- 
mate that  a  5-inch  slab  (or  d  =  4)  will  carry  the  load.  This 
will  weigh  60  pounds  per  square  foot,  and  make  a  total  live  and 
dead  load  of  210  pounds  per  square  foot.  A  strip  1  foot 
wide  and  8  feet  long  will  carry  a  total  load  of  1,680  pounds, 
and  its  moment  will  be  i  X  1,680  X  96  =  20,160  inch-pounds. 


/• 

\             BEflM  a                         /• 

^ 

J 

J                                                     V 

GIRDER  d              QIRDER^ 

7^ 

: 

> 

BEAM  b 

r 

-\           BEftM  C                         ( 

<i) 

J 

i             ~t^o-            / 

} 

" 

Fig.  26.    Skeleton  Outline  of  Floor  Panel 

Showing  Slab,  Beam,  and  Girder 

Construction 


98  REINFORCED  CONCRETE 

Using  the  first  half  of  Equation  (12),  we  can  substitute  the 
known  values,  and  say  that 

20,160  =  |  X  600  X  12  X  .385  d  X  .872  d 

=  1,209  d2 
d2  =  16.67 
d  =    4.08  in. 

In  this  case  the  span  of  the  slab  is  considered  as  the  distance 
from  center  to  center  of  the  beams.  This  is  evidently  more 
nearly  exact  than  to  use  the  net  span  (which  equals  8  feet, 
less  the  still  unknown  width  of  beam),  since  the  true  span  is 
the  distance  between  the  centers  of  pressure  on  the  two  beams. 
It  is  likely  that  the  true  span  (really  indeterminable)  will  be 
somewhat  less  than  8  feet,  which  will  probably  justify  using 
the  round  value  of  c?  =  4  inches,  and  the  slab  thickness  as  5 
inches,  as  first  assumed.  The  area  of  the  steel  per  inch  of  width 
of  the  slab  equals  pbd  =  .01  X  1  X  4.08  =  .0408  square  inch. 
Using  i-inch  round  bars  whose  area  equals  .1963  square  inch, 
the  required  spacing  of  the  bars  will  be  .1963  -*-  .0408  =  4.81 
inches.  As  shewn  later,  the  girder  will  be  11  inches  wide,  and 
the  net  width  of  the  slab  is  240  inches  less  11  inches  or  229 
inches.  229  •+•  4.81  =  47.6,  call  it  48,  the  number  of  bars  to  be 
spaced  equally  in  one  panel. 

Beam.  The  load  on  a  beam  is  that  on  an  area  of  8  feet  by  20 
feet,  and  equals  8  X  20  X  210  =  33,600  pounds  for  live  and 
dead  load.  As  a  rough  trial  value,  we  shall  assume  that  the 
beam  will  be  12  inches  wide  and  15  inches  deep  below  the  slab, 
having,  that  is,  a  volume  of  1  X  1.25  X  20  =  25  cubic  feet, 
which  will  weigh  3,600  pounds.  Adding  this,  we  have  37,200 
pounds  as  the  total  live  and  dead  load  carried  by  each  beam. 
The  load  is  uniformly  distributed  and  the  moment  is 

M  =  i.  x  37,200  X  240  =  1,116,000  in.-lb. 

o 

We  shall  assume  that  the  beam  is  to  have  a  depth  d  to  the  rein- 
forcement of  22  inches.  Substituting  the  known  quantities  in 
the  approximate  equation,  M8  =  As(d  —  kt),  which  may  be 


REINFORCED  CONCRETE  99 

used,  when  we  may  be  sure  that  the  neutral  axis  is  within  the 
slab,  we  have 

1,116,000  =  AX  16,000  X  (22  —  1.67) 
A  =  3.43  sq.  in. 

For  T-beams  with  very  wide  slabs  and  great  depth  of  beam,  the 
percentage  of  steel  is  always  very  small.  In  this  case,  p  = 
3.43  -*-  (96  X  22)  =  .00162.  Such  a  value  is  beyond  the  range 
of  those  given  in  Table  XI.  We  must,  therefore,  compute  the 
value  of  k  from  Equation  (6),  and  we  find  that  k  =  .180, 
and  kd  =  3.96,  which  shows  that  the  neutral  axis  is  within  the 
slab ;  x  =  J  kd  =  1.32,  and,  therefore,  jd  =  20.68.  Assume  that 
&'  equals  fourteen  times  the  slab  thickness,  or  70  inches.  (See 
page  90.)  Substituting  these  values  in  the  upper  part  of 
Equation  (12)  in  order  to  find  the  value  of  c,  we  find  that 
c  =  390  pounds  per  square  inch.  Substituting  the  known  values 
in  the  second  half  of  Equation  (12),  to  obtain  a  more  precise 
value  of  s,  we  find  that  s  =  15,734  pounds  per  square  inch. 

The  required  area  (3.43  square  inches)  of  the  bars  will  be 
afforded  by  six  i-inch  round  bars  (6  X  .60  =  3.60)  with  consid- 
erable to  spare.  From  Table  XVIII  we  find  that  six  1-inch 
bars,  either  square  or  round,  if  placed  in  one  row,  would  require 
a  beam  14.72  inches  wide.  This  is  undesirably  wide,  and  so  we 
shall  use  two  rows,  three  in  each  row,  and  make  the  beam  9 
inches  wide.  This  will  add  an  inch  to  the  depth,  and  the  total 
depth  will  be  22  +  3  =  25  inches.  The  concrete  below  the  slab 
is  therefore  9  inches  wide  by  20  inches  deep,  instead  of  12 
inches  wide  by  15  inches  deep,  as  assumed  when  computing  the 
dead  load,  but  the  weight  is  the  same.  It  should  also  be  noted 
that  the  span  of  these  beams  was  considered  as  20  feet,  which  is 
the  distance  from  center  to  center  of  the  columns  (or  of  the 
girders).  This  is  certainly  more  nearly  correct  than  to  use  the 
net  span  between  the  columns— or  girders— which  is  still  un- 
known, since  neither  columns  nor  girders  are  yet  designed. 
Probably  a  20-foot  span  gives  some  margin  of  safety. 

Girder.  The  load  on  one  beam  is  computed  above  as  37,200 
pounds.  The  load  on  the  girder  is,  therefore,  the  equivalent  of 
this  load  concentrated  at  the  center,  or  of  double  the  load  (74,400 


100  REINFORCED  CONCRETE 

pounds)  uniformly  distributed.  If  for  a  trial  value  it  is 
assumed  that  the  girder  will  be  12  inches  by  22  inches  below  the 
slab,  its  weight  for  sixteen  feet  will  be  4,224  pounds.  This 
gives  a  total  of  78,624  pounds  as  the  equivalent  total  live  and 
dead  load  uniformly  distributed  over  the  girder.  Its  moment 
in  the  center,  therefore,  equals  -J  X  78,624  X  192  =  1,886,976 
inch-pounds. 

The  width  of  the  slab  in  this  case  is  almost  indefinite,  being 
20  feet,  or  forty-eight  times  the  thickness  of  the  slab.  We  shall 
therefore  assume  that  the  compression  is  confined  to  a  width  of 
fourteen  times  the  slab  thickness,  or  that  b'  =  70  inches.  Assume 
for  a  trial  value  that  d  =  25  inches ;  then  from  the  approxi- 
mate equation  Ms  =  As  (d  —  &t),  if  s  =  16,000.  we  find  that 
A  =  5.05  square  inches.  Then  p  =  .00288 ;  and,  from  Equation 
(6),  A;  =  .231,  and  kd  =  5.775.  This  shows  that  the  neutral 
axis  is  below  the  slab,  and  that  it  belongs  to  Case  I,  page  88. 
Checking  the  computation  of  kd  from  Equation  (16),  we  com- 
pute kd  =  5.82,  which  is  probably  the  more  nearly  correct  value 
because  computed  more  directly.  The  discrepancy  is  due  to  the 
dropping  of  decimals  during  the  computations.  From  Equation 
(15),  we  compute  that  x  =  1.87,  then  (d  —  x]  =23.13.  Sub- 
stituting the  value  of  the  moment  and  of  the  dimensions  in  the 
upper  part  of  Equation  (17),  we  compute  c  equal  to  409 
pounds  per  square  inch.  Similarly,  making  substitutions  in  the 
lower  part  of  Equation  (17),  using  the  more  precise  value  of 
(d  —  x)  for  the  lever  arm  of  the  steel, 'we  find  s  =  16,052  pounds 
per  square  inch.  (The  student  should  verify  in  detail  all  these 
computations.) 

The  total  required  area  of  5.08  square  inches  may  be  divided 
into,  say,  eight  round  bars  I-inch  in  diameter.  These  would  have 
an  area  of  4.81  square  inches.  The  discrepancy  is  about  5  per 
cent.  Using  the  eight  round  f-inch  bars,  the  unit  stress  would 
be  nearly  17,000  pounds.  If  this  is  considered  undesirable,  an 
area  more  nearly  exact  may  be  obtained  by  using  six  round 
1-inch  bars  and  two  round  1-inch  bars.  The  area  would  be  5.18 
square  inches,  somewhat  in  excess  of  that  required.  These  bars, 
placed  in  two  rows,  would  require  that  the  beam  be  at  least  10.78 


REINFORCED  CONCRETE  101 

inches  wide.  We  shall  call  it  11  inches.  The  total  depth  of  the 
beam  will  be  3  inches  greater  than  d,  or  28  inches.  This  means 
23  inches  below  the  slab,  and  the  area  of  concrete  below  the  slab 
is  therefore  11  X  23  =  253  square  inches,  rather  than  12  X  22  = 
264  square  inches,  as  assumed  for  trial. 

Shear.  The  shearing  stresses  between  the  rib  and  slab  of 
the  girder  are  of  special  importance  in  this  case.  The  quantity 
Sh,  page  94,  equals  the  total  compression  in  the  concrete,  which 
equals  the  total  tension  in  the  steel,  which  equals,  in  this  case, 
16,052  X  5.08  =  81,544  pounds.  This  equals  3  bzL,  in  which 
b  =  11,  L  =  16  (feet),  and  z  is  to  be  determined. 

z  =  81,544  -5-  (3  X  11  X  16)  =  154  Ib.  per  sq.  in. 

This  measures  the  maximum  shearing  stress  under  the  slab,  and 
is  almost  safe,  even  without  the  assistance  furnished  by  the 
stirrups  and  the  bars,  which  would  come  up  diagonally  through 
the  ends  of  the  beam— where  this  maximum  shear  occurs— nearly 
to  the  top  of  the  slab.  The  vertical  planes  on  each  side  of  the  rib 
have  a  combined  width  of  10  inches,  and  therefore  the  unit  stress 
is  T£  X  154  =  169  pounds  per  square  inch.  This  is  a  case  of  true 
shear,  though  it  is  somewhat  larger  than  the  permissible  work- 
ing shear.  But  there  are  still  other  shearing  stresses  in  these 
vertical  planes.  In  the  case  of  a  strip  of  the  slab,  say,  one  foot 
wide,  which  is  reinforced  by  slab  bars  parallel  to  the  girder,  the 
elasticity  of  such  a  strip  (if  disconnected  from  the  girder)  would 
cause  it  to  sag  in  the  center.  This  must  be  prevented  by  the 
shearing  strength  of  the  concrete  in  the  vertical  plane  along  each 
edge  of  the  girder  rib.  On  account  of  the  combined  shearing- 
stresses  along  these  planes,  it  is  usual  to  specify  that  when 
girders  are  parallel  with  the  slab  bars,  bars  shall  be  placed  across 
the  girder  and  through  the  top  of  the  slab  for  the  special  purpose 
of  resisting  these  shearing  stresses.  Some  of  the  stresses  are 
indefinite,  arid  therefore  no  precise  rules  can  be  computed  for 
the  amount  of  the  reinforcement.  But  since  the  amount  required 
is  evidently  very  small,  no  great  percentage  of  accuracy  is  im- 
portant. Specifications  on  this  point  usually  require  f -inch 
bars,  5  feet  long,  spaced  12  inches  apart. 


102 


REINFORCED  CONCRETE 


The  shear  of  the  girder,  taken  as  a  whole,  should  be  computed 
as  for  simple  beams,  already  discussed.  Stirrups  also  should  be 
used. 

Another  special  form  of  shear  must  be  considered  in  this 
problem.  Where  the  beams  enter  the  girder,  there  is  a  tendency 
for  the  beams  to  tear  their  way  out  through  the  girder.  The 
total  load  on  the  girder  by  the  two  beams  on  each  side  is  of 
course  equal  to  the  total  load  on  one  beam,  in  this  case  37,200 
pounds.  Some  of  the  reinforcing  bars  of  the  beam  will  be  bent 
up  diagonally  so  that  they  enter  the  girder  near  its  top,  and 
therefore  the  beam  could  not  tear  out  without  shearing  through 
the  girder  from  near  its  top  or  for  a  depth  of,  say,  22  inches 
(3  inches  less  than  d).  If  there  were  no  reinforcing  steel  in  the 
girder  and  enough  load  were  placed  on  the  beam  to  actually  tear 

it  out,  the  fracture  would  evi- 
dently be  in  the  form  of  an  in- 
verted V.  The  resistance  to  such 
tearing  out  would  be  chiefly  that 
of  the  tensile  strength  of  the  con- 
crete. If  the  width  of  the  frac- 
ture (or  its  horizontal  projection) 
is  assumed  to  be  44  inches,  and 
the  other  dimension,  which  is  the 
width  of  the  girder  rib,  11  inches, 
there  is  an  area  of  484  square 
inches;  and  at  40  pounds  working  tension,  it  could  safely  carry 
a  load  of  19,360  pounds.  But  the  total  load,  as  shown  above,  is 
37,200  pounds.  The  steel  reinforcement  of  the  girder  is,  there- 
fore, essential  to  safety.  Although  the  main  reinforcing  bars 
of  the  girder  would  have  to  be  torn  out  before  complete  failure 
could  take  place,  the  resistance  to  a  small  displacement,  per- 
pendicular to  the  bars,  is  comparatively  slight,  and  therefore 
these  bars  should  not  be  depended  on  to  resist  this  stress.  But 
a  pair  of  ordinary  vertical  stirrups,  passing  under  the  main 
girder  bars,  b  b,  Fig.  27,  can  easily  be  made  of  such  size  as  to 
take  any  desired  portion,  or  all,  of  that  load.  The  stirrups 
should  be  bent  at  the  upper  end  so  that  the  strength  of  the 


Fig.  27.    Details  of  Reinforce- 
ment at  Junction  of  Beam 
and  Girder 


REINFORCED  CONCRETE 


103 


bars  may  be  developed  without  dependence  upon  bond  adhesion. 
Although  precise  numerical  calculations  are  impossible  without 
making  assumptions  which  are  themselves  uncertain,  the  follow- 
ing calculation  is  probably  safe.  37,200  —  19,360  =  17,840; 


c 


C 


—i *-A       f  'tn  *r*-i       i^i,        iti         t          '  'il  '         t        it  I     i  i      i  *ttt  T  T  '  -\ 

F^TT        \uTT     TT 


for  s  =  16,000,  the  required  area  would  be  1.115  square  inches. 
Two  pairs  of  stirrups  would  give  four  bar  areas  which  could 
each  be  0.28  square  inch,  and  this  amount  of  reinforcement 
would  be  amply  provided  by  f-inch  round  bars.  Fig.  28,  which 
illustrates  a  complete  floor  panel,  shows  nearly  all  these  various 
details  gathered  ^together. 


104  REINFORCED  CONCRETE 

MISCELLANEOUS  CONCRETE  DESIGNS 
SIMPLE  FOOTINGS 

Effectiveness  of  Reinforced  Concrete  Footings.  When  a 
definite  load,  such  as  a  weight  carried  by  a  column  or  wall,  is  to 
be  supported  on  a  subsoil  whose  bearing  power  has  been  esti- 
mated at  some  definite  figure,  the  required  area  of  the  footing 
becomes  a  perfectly  definite  quantity,  regardless  of  the  method 
of  construction  of  the  footing.  But  with  the  area  of  the  footing 
once  determined,  it  is  possible  to  effect  considerable  economy  in 
the  construction  of  the  footing,  by  the  use  of  reinforced  con- 
crete. An  ordinary  footing  of  masonry  is  usually  made  in 
pyramidal  form,  although  the  sides  are  stepped  off  instead  of 
being  made'  sloping.  It  may  be  stated  that  the  depth  of  the 
footing  below  the  base  of  the  column  or  wall,  when  ordinary 
masonry  is  used,  nrnst  be  practically  equal  to  the  width  of  the 
footing.  The  offsets  in  the  masonry  cannot  ordinarily  be  made 
any  greater  than  the  heights  of  the  various  steps.  Such  a  plan 
requires  an  excessive  amount  of  masonry. 

Wall  Footing.  Assume  that  a  24-inch  wall,  with  a  total  load 
of  42,000  pounds  per  running  foot,  is  to  rest  on  a  soil  which  can 
safely  bear  a  load  of  7,000  pounds  per  square  foot.  The  re- 
quired width  of  footing  is  6  feet.  The  footing  will  project  2 
feet  on  either  side  of  the  wall.  For  each  lineal  foot  of  the  wall 
and  on  each  side,  there  is  an  inverted  cantilever,  with  an  area 
2  feet  X  1  foot,  and  carrying  a  load  of  14,000  pounds.  The 
center  of  pressure  is  12  inches  from  the  wall ;  the  moment  about 
a  section  through  the  face  of  the  wall  is  12  X  14,000  =  168,000 
inch-pounds.  Using  a  grade  of  concrete  such  that  M  —  95  bd2, 
p  =  .00675,  and  j  =  .88,  then  with  b  =  12,  we  have 

d2  =  M  -*-  95  b 

=  168,000  •+•  1,140  =  147.4 
d  =12.15  in. 

The  amount  of  steel  required  per  inch  of  width  will  equal 
.00675  X  12.15  =  .082  square  inch,  which  may  be  supplied  by 
f-inch  bars  spaced  about  7  inches  on  centers.  A  total  thickness 
of  15  inches  will  therefore  fulfil  the  requirements.  Theoretically, 


REINFORCED  CONCRETE  105 

this  thickness  could  be  reduced  to  8  or  even  6  inches  at  the  outer 
edge,  since  there  the  moment  and  the  shear  both  reduce  to  zero. 
But  when  the  concrete  is  used  very  wet  and  soft,  it  cannot  be  laid 
with  an  upper  surface  of  even  moderate  slope  without  using 
forms  to  confine  it,  and  in  the  case  just  given  such  forms  would 
cost  more  than  would  be  saved  in  the  concrete. 

Shear.  The  shear  (V)  on  a  vertical  section  directly  under 
the  face  of  the  wall,  and  12  inches  long,  is  14,000  pounds. 
Applying  Equation  (13) 

v  =  V-*~  bjd 

=  14,000  •*-  (12  X  .88  X  12.15) 
=  109  Ib.  per  sq.  in. 

This  is  far  greater  than  a  safe  working  stress  and  the  slab  might 
fail  from  diagonal  tension.  When  a  loaded  beam  is  supported 
freely  at  each  end,  the  maximum  shear  is  found  at  the  ends 
where  the  moment  is  minimum,  and  some  of  the  bars  which  are 
not  needed  there  for  moment  may  be  bent  up  so  as  to  resist  the 
shear.  Unfortunately,  in  the  case  of  a  cantilever,  the  maximum 
moment  and  maximum  shear  are  found  at  the  same  beam  sec- 
tion—in this  case,  at  the  face  of  the  wall.  Therefore,  if  the 
concrete  itself  cannot  carry  the  shear,  additional  steel  must  be 
used  to  do  that  work.  Bars  inclined  about  4.5  degrees  serve 
the  purpose  most  economically,  provided  they  are  secured  against 
slipping  and  can  develop  their  full  strength.  This  may  be  done 
by  extending  them  through  the  column  and  by  bending  the  free 
ends.  Assume  that  the  concrete  alone  takes  up  40  pounds  of  the 
109  pounds  shear,  found  above,  or  37  per  cent.  This  leaves  63 
per  cent  to  be  taken  by  the  steel  bars.  14,000  X  .63  =  8,820 
pounds  per  foot  or  735  pounds  per  lineal  inch.  The  only  prac- 
ticable arrangement  is  to  alternate  these  bars  with  the  moment 
bars  and  therefore  space  them  7  inches  apart.  Then  each  bar 
must  take  up  7  X  735  =  5,145  pounds  of  shear.  A  fVinch 
square  bar  will  safely  sustain  that  stress.  Such  a  bar  has  a 
perimeter  of  2.25  inches.  At  75  pounds  per  square  inch  for 
bond  adhesion  (plain  bars),  each  lineal  inch  of  the  bar  would 
have  a  working  adhesion  of  169  pounds.  Dividing  5,145  by  this 


106 


REINFORCED  CONCRETE 


gives  30  inches,  the  required  length  of  bar  beyond  any  point 
where  the  stress  is  as  much  as  5,145  pounds.  Since  there  is  not 
that  length  of  bar  available,  bond  adhesion  cannot  be  relied  on 
and  the  bars  must  be  bent,  as  shown  in  Fig.  29.  Even  a  deformed 
bar,  although  a  good  type  may  be  used  with  working  adhesion 
about  double  that  of  a  plain  bar,  would  need  to  be  longer  than 
space  permits,  if  straight,  and  it  should  be  hooked. 

Bond  Adhesion  in  Moment  Bars.     The  steel  required  per  inch 
of  width  is  .082  square  inch,  and  in  7  inches,  .574  square  inch. 

Since  the  design  calls 
for  a  unit  tension  of 
16,000  pounds  in  the 
steel,  the  actual  tension 
in  the  bar  will  be  16,000 
X  .574  =  9,184  pounds. 
A  f-inch  square  bar  has 
a  perimeter  of  3  inches 
and,  at  75  pounds  per 
square  inch,  can  furnish 
a  working  bond  adhe- 
sion of  225  pounds  per 
lineal  inch  of  bar.  But 
this  would  need  9,184  -*- 
225  =  41  inches,  the  re- 
quired length  beyond 
the  face  of  the  wall. 
If  150  per  square  inch 

bond     adhesion     is     al- 
Fig.  29.    Diagram  of  Footing  for  a  Wall       lowfid   f Qr   &   good   type 

of  deformed  bar,  the  required  length,  computed  similarly,  would 
be  a  little  over  20  inches,  and  as  this  is  less  than  the  24-inch 
cantilever,  straight  deformed  bars  will  do.  The  designer,  there- 
fore, has  the  choice  of  using  a  hook  on  each  end  of  plain  bars, 
as  illustrated  in  Fig.  29,  or  using  straight  deformed  bars, 
which  would  be  cheaper  at  the  usual  relative  prices. 

Column  Tooting.    The  most  common  method  of  reinforcing  a 
simple  column  footing  is  shown  in  Fig.  30.     Two  sets  of  the 


6-0 


REINFORCED  CONCRETE 


107 


V 


65' 


reinforcing  bars  are  at  a-a  and  b-b}  and  are  placed  only  under 
the  column.  To  develop  the  strength  of  the  corners  of  the 
footings,  bars  are  placed  diagonally  across  the  footing,  as  at 
c-c  and  d-d..  In  designing  this  footing,  the  projections  of  the 
footing  beyond  the  column  are  treated  as  free  cantilever  beams, 
or  by  the  method  discussed  above.  The  maximum  shear  occurs 
near  the  center ;  and  therefore,  if  this  shear  must  be  taken  care 
of  by  reinforcement, 
stirrups  or  bent  bars 
should  be  used. 

Example.  Assume  that  a 
load  of  300,000  pounds  is 
to  be  carried  by  a  column 
28  inches  square,  on  a  soil 
that  will  safely  carry  a 
load  of  6,000  pounds  per 
square  foot.  The  reinforc- 
ing bars  are  to  run  diag- 
onally and  directly  across 
the  footing,  Fig.  30.  What 
should  be  the  dimensions 
of  the  footing  and  the  size 
and  spacing  of  the  bars? 
Also  investigate  the  shear. 

Solution.  The  load  of 
300,000  pounds  will  evi- 
dently require  an  area  of 
50  square  feet.  The  sides 
of  the  square  footing  will 
evidently  be  7.07  feet,  or, 
say,  85  inches ;  and  the 
offset  on  each  side  of  the 
28-inch  column  is  28.5 
inches.  The  area  of  each 
cantilever  wing  which  is 
straight  out  from  the  col- 
umn is  28.5  X  28  =  798 
square  inches  or  5.54 
square  feet.  The  load  is, 
therefore,  5.54  X  6,000  =  33,240  pounds.  Its  lever  arm  is  one-half  of 
28.5  inches,  or  14.25  inches.  The  moment  is  therefore  473,812  inch- 
pounds.  Adopting  the  straight-line  formula,  M  =  95  bd8,  on  the  bagis 
that  p  =  .00675,  we  may  write  the  equation 


28.5*+ 


0  n  n  n  n  n 


Fig.  30.    Diagram  of  Footing  for  a  Column 


Therefore 


473,812  =  05  x  28  X  d2 
d-'=  178 
d=13.3  in. 

'==  p  b  d  =  .00675  X  28  X  13.3 
=  2.51  sq.  in. 


This  area  of  metal  may  be  furnished  by  six  i-inch  round  bars,  and 
therefore  there  should  be  six  1-inch  round  bars  spaced  about  4.5 
inches  apart  under  the  column  in  both  directions,  a-a  and  &-&. 


108  REINFORCED  CONCRETE 

Corner  Sections.  The  mechanics  of  the  reinforcements  of  the  corner 
sections,  which  are  each  28.5  inches  square,  is  exceedingly  complicated 
in  its  precise  theory.  The  following  approximation  to  it  is  probably 
sufficiently  exact.  The  area  of  each  corner  section  is  the  square  of 
28.5  inches,  or  812.25  square  inches.  At  6,000  pounds  per  square  foot, 
the  pressure  on  such  a  section  is  33,844  pounds,  and  the  center  of 
gravity  of  this  section  is,  of  course,  at  the  center  of  the  square,  which 
is  14.25  X  1.414  =  20.15  inches  from  the  corner  of  the  column.  A  bar 
immediately  under  this  diagonal  line  would  have  a  lever  arm  of  20.15 
inches.  A  bar  parallel  to  it  would  have  the  same  lever  arm  from  the 
middle  of  the  bar  to  the  point  where  it  passes  under  the  column. 
Therefore,  if  we  consider  that  this  entire  pressure  of  33,844  pounds  has 
an  average  lever  arm  of  20.15  inches,  we  would  have  a  moment  of 
681,957  inch-pounds.  Using,  as  before,  the  moment  equation  M  =  95  &d2, 
we  may  transpose  this  equation  to  read 


95  d2 
Then 


ft 

95  X  14.5 

=  3.34  sq.  in. 

This  area  of  steel  will  be  furnished  by  six  |-inch  square  bars.  The 
diagonal  reinforcement  will  therefore  consist  of  six  2-inch  square  bars 
running  diagonally  in  both  directions.  These  bars  should  be  spaced 
about  5  inches  apart.  Those  that  are  nearly  under  the  diagonal  lines 
of  the  square  should  be  about  9  feet  8  inches  long  ;  those  parallel  to 
them  will  each  be  10  inches  shorter  than  the  next  bar. 

Bond  Adhesion.  The  total  tension  in  the  steel  of  the  a  and  b  bars  is 
16,000  X  2.51  =  40,160  pounds,  or  6,093  pounds  per  bar,  which  is  found 
at  a  point  immediately  under  the  column  face.  There  will  be  28.5  inches 
length  of  steel  in  each  bar  from  the  column  face  to  the  edge  of  the  slab, 
and  this  will  require  a  bond  adhesion  of  6,693  -r-  28.5  =  235  pounds  per 
lineal  inch.  Referring  to  Table  XVII,  we  see  that  this  unit  value  is 
greater  than  a  proper  working  value  for  1-inch  plain  round  bars  but  is 
safe  for  |-inch  deformed  round  bars.  Making  a  similar  calculation  for 
the  diagonal  bars,  the  stress  in  each  one  is  (16,000  X  3.34)  -^  6  =  8,907 
pounds.  The  length,  practically  uniform  for  all,  beyond  the  face  of 
the  column  is  40  inches,  which  will  require  a  bond  adhesion  of  223 
pounds  per  lineal  inch.  This  is  just  within  the  limit  for  1-inch  plain 
square  bars. 

It  should  be  noted  from  the  solution  of  this  and  the  previous 
problem  that,  on  account  of  the  combination  of  heavy  load  and 
small  cantilever  projection,  the  bond  adhesion  of  footings  is 
always  a  critical  matter  and  its  investigation  should  never  be 
neglected.  It  frequently  happens,  as  above  illustrated,  that  the 
greater  bond  resistance  of  deformed  bars  will  permit  the  use 


REINFORCED  CONCRETE  109 

of  a  certain  bar  which  is  safe  for  the  moment  resistance  when 
the  same  size  of  plain  bar  cannot  be  used.  Since  smaller  bars 
have  a  greater  surface  and  a  greater  adhesion  per  unit  both 
of  area  and  of  strength  than  larger  bars,  the  requisite  adhesion 
may  sometimes  be  obtained  by  using  a  proportionately  larger 
number  of  smaller  bars.  When  neither  method  will  produce  the 
required  adhesion,  the  bars  should  be  bent  into  a  hook,  which 
should  be  a  full  semicircle  with  a  diameter  about  8  to  12  times 
the  diameter  of  the  bar. 

Shear.  The  "punching"  shear  on  the  slab  is  measured  by  the 
upward  pressure  on  that  part  of  the  slab  which  is  outside  of  the 
column  area.  This  equals  852— 282  =  6,441  square  inches,  or 
44.73  square  feet.  Multiplying  by  6,000  we  have  268,380 
pounds.  The  resisting  area  equals  the  perimeter  of  the  column 
times  jd,  which  here  is  4  X  28  X  .88  X  13.3  =  1,311  square 
inches.  Dividing  268,380  by  this,  we  have  204  pounds  per 
square  inch.  If  the  column  and  slab  were  made  of  plain  con- 
crete, this  figure  would  be  considered  too  high  for  working- 
stress,  120  pounds  being  usually  allowed.  In  this  case,  an  actual 
punching  of  the  slab  would  require  that  48  sections  of  f-inch 
round  bars  should  be  sheared  off.  If  the  concrete  actually 
takes  an  average  of  120  pounds  per  square  inch  on  1,311  square 
inches  of  surface,  the  concrete  would  take  up  157,320  pounds, 
leaving  111,060  pounds  for  the  48  bars,  or  2,314  pounds  for 
each  bar.  Dividing  by  the  bar  area,  we  have  a  shearing  stress 
of  5,237  pounds  per  square  inch  of  bar  section,,  which  is  insig- 
nificant for  the  steel  and  is  amply  safe,  provided  that  any  such 
shearing  stress  as  2,314  pounds  per  bar  could  be  developed 
before  the  concrete  itself  were  crushed  by  the  bars.  Consider- 
ing the  various  forces  resisting  the  punching  action,  and  also 
that  even  the  204  pounds  per  square  inch  is  far  short  of  the 
ultimate  value  of  true  shear,  the  design  is  probably  safe, 
although  the  factor  of  safety  is  probably  low.  If  further 
reinforcement  were  considered  necessary,  it  could  be  added  in 
the  form  of  bent  bars,  as  in  the  previous  problem. 

It  is  impracticable  to  develop  a  true  rational  formula  for  the 
computation  of  the  diagonal  tension  in  slabs  which  support 


110  REINFORCED  CONCRETE 

columns,  but  several  elaborate  tests*  by  Professor  Talbot  show 
that  the  following  method  gives  results  which  are  reasonably 
consistent  and  also  comparable  with  the  corresponding  results 
for  ordinary  beams.  Consider  a  section  through  the  slab  all 
the  way  around  the  column  and  at  a  distance  d  from  the 
face  of  the  column,  and  apply  Equation  (13),  v  =  V-*-bjd. 
In  this  case  the  section  would  be  a  square  (2  X  13.3)  +28  = 
54.6  inches  on  a  side.  The  area  is  2,981  square  inches.  The 
area  of  the  whole  footing  is  852= 7,225  square  inches,  and  the 
area  outside  this  square  is  7,225  —  2,981  =  4,244  square  inches, 
or  29.5  square  feet.  29.5  X  6,000  =  177,000  pounds  =  V; 
b  is  the  perimeter  of  the  square  and  equals  4  X  54.6  =  218.4; 
jd  is  .88  X  13.3  =  11.7.  Then  v  =  69.  Since  this  is  higher 
than  40,  the  usual  permissible  working  stress  when  taken 
as  a  measure  of  unreinforced  diagonal  tension,  it  shows  that 
bent  bars  or  stirrups  must  be  used,  but  in  either  case  the 
reinforcement  need  carry  only  the  extra  29  pounds  per  square 
inch.  Multiplying  this  by  jd,  we  have  29  X  11.7  =  339,  the 
required  assistance  in  pounds  per  lineal  inch.  If  a  bar  is 
placed  every  4.5  inches  (corresponding  with  the  main  rein- 
forcing bars)  the  stress  per  bar  will  be  1,525  pounds,  which  at 
16,000  pounds  unit  stress  will  require  .095  square  inches  or  a 
fk-inch  square  bar.  Perhaps  the  most  convenient  form  of 
reinforcement  in  this  case  would  be  a  series  of  stirrups  made 
by  a  continuous  bar,  i5s  inch  square,  which  zigzags  up  and 
down  with  an  amplitude  equal  to  jd  or  11.7  inches,  and  so  that 
there  is  a  bar  up  or  down  at  every  4.5  inches.  This  should  be 
located  at  the  "critical  section"  at  a  distance  d  equal  to  13.3 
inches  from  the  column  face.  It  will  require  a  bar  about  16 
feet  6  inches  long  to  make  the  continuous  stirrup  for  each  side 
of  the  square.  Each  bar  must  be  bent  with  about  eleven  semi- 
circular bends,  as  shown  in  Fig.  30,  so  placed  that  each  down- 
ward loop  will  pass  under  one  of  the  main  reinforcing  bars. 
The  loops  at  the  top  preclude  all  possibility  of  bond  failure. 

Since  the  shear  decreases  to  zero  at  the  edge  of  the  slab,  and 
the  distance  from  the  stirrup  to  the  edge  of  the  slab  is  only  a 

*  Bulletin  No.  67,  University  of  Illinois. 


REINFORCED  CONCRETE  111 

little  more  than  the  thickness  of  the  slab,  it  is  apparent  without 
calculation  that  no  further  shear  reinforcement  is  needed. 

Continuous  Beams.  Continuous  beams  are  sometimes  used 
to  save  the  expense  of  underpinning'  an  adjacent  foundation 
or  wall.  These  footings  are  designed  as  simple  beams,  but  the 
steel  is  placed  in  the  top  of  the  beams. 

Illustrative  Example.  Assume  that  the  columns  on  one  side 
of  a  building  are  to  be  supported  by  a  continuous  footing; 
that  the  columns  are  22  inches  square,  spaced  12  feet  on  center ; 
and  that  they  support  a  load  of  195,000  pounds  each.  If  the 
soil  will  safely  support  6,000  pounds  per  square  foot,  the  area 
required  for  a  footing  will  be  195,000  -*•  6,000  =  32.5  square 
feet.  Since  the  columns  are  spaced  12  feet  apart,  the  width 
of  footing  will  be  32.5  -*- 12  =  2.71  feet,  or  2  feet  9  inches. 
To  find  the  depth  and  amount  of  reinforcement  necessary  for 
this  footing,  it  is  designed  as  a  simple  inverted  beam  supported 
at  both  ends  (the  columns),  and  loaded  with  an  upward  pres- 
sure of  6,000  pounds  per  square  foot  on  a  beam  2  feet  9  inches 
wide.  In  computing  the  moment  of  this  beam,  the  continuous- 
beam  principle  may  be  utilized  on  all  except  the  end  spans, 
and  thus  the  moment  may  be  reduced  and,  therefore,  the 
required  dimensions  of  the  beam. 

COMPOUND  FOOTINGS 

Conditions  Demanding  Compound  Footings.  When  a 
simple  footing  supports  a  single  column,  the  center  of  pressure 
of  the  column  must  pass  vertically  through  the  center  of  grav- 
ity of  the  footing,  or  there  will  be  dangerous  transverse  stresses 
in  the  column,  as  is  discussed  later.  It  is,  however,  sometimes 
necessary  to  support  a  column  on  the  edge  of  a  property  when 
it  is  nbt  permissible  to  extend  the  foundations  beyond  the 
property  line,  and  in  such  a  case,  a  simple  footing  is  imprac- 
ticable. The  method  of  solution  to  be  used  is  indicated  in 
Fig.  31.  .  The  nearest  interior  column  (or  even  a  column  on 
the  opposite  side  of  the  building,  if  the  building  is  not  too 
wide)  is  selected,  and  a  combined  footing  is  constructed  under 
both  columns.  The  weights  on  the  two  columns  are  computed. 


112 


REINFORCED  CONCRETE 


If  they  are  equal,  the  center  of  gravity  is  halfway  between 
them;  if  unequal,  the  center  of  gravity  is  on  the  line  joining 
their  centers,  and  at  a  distance  from  them  such  that, 
x:y::W2:W1,  Fig.  31.  In  this  case,  evidently  W2  is  the 


The  area  abdc  must  fulfil  two  conditions: 

*),  divided  by  the 


greater  weight. 

(1)  The  area  must,  equal  the  total  loading 
allowable  loading  per  square  foot. 

(2)  The  center  of  gravity  must  be  located  at  0. 

Practical  Treatment  of  Problem.  An  analytical  solution 
for  all  cases  of  the  relative  and  absolute  values  of  ab  and  cd 
which  will  fulfil  the  two  conditions  is  very  difficult.  Sometimes 


* 

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Q 

a 

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forcing  Bars  |! 

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. 

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1 

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W2- 

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tS 

^1  Hi 

I, 

II 

J^> 

i 

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\\ 

SO  Bars 

N: 
Eqt. 

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1! 

j! 

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t 

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MH 

Fig.  31.   Combined  Footing  for  Two  Columns, 
One  on.  Edge  of  Property 

the  only  practicable  solution  is  to  obtain,  by  trial  and  adjust- 
ment, a  set  of  dimensions  which  will  be  sufficiently  accurate  for 
practical  purposes.  It  usually  happens  that  an  inner  column 
of  a  building  carries  a  greater  load  than  an  outer  column. 
This  facilitates  the  solution,  for  then,  as  in  the  example  given 
below,  the  footing  may  be  extended  beyond  the  inner  column 
and  may  be  made  approximately  rectangular. 

Illustrative  Example.  A  column,  Wlt  carrying  400,000 
pounds,  is  to  be  located  on  the  edge  of  a  property  and  another 
column,  W2,  carrying  600,000  pounds,  is  located  16  feet  from 
it.  Assume  that  the  subsoil  can  sustain  safely  7,000  pounds 


REINFORCED  CONCRETE  113 

per  square  foot.  We  are  to  determine  the  shape  and  design 
of  the  footing1. 

Assume  that  the  footing-  slab  weighs  400  pounds  per  square 
foot  of  surface;  then  the  net  effective  upward  pressure  of  the 
subsoil  which  will  support  the  column  equals  7,000  —  400  — 
6,600  pounds  per  square  foot.  For  simplicity  of  calculation, 
the  computations  involving  soil  pressures  and  slab  areas  will 
generally  use  the  units,  feet  -and  decimals.  The  change  to  feet 
and  inches  can  be  made  when  the  final  dimensions  have  been 
computed.  * 

The  total  column  load  is  1,000,000  pounds;  at  6,600  pounds 
per  square  foot  the  area  must  be  151.515  square  feet.  Assume 
(hat  the  TF0  column  is  .2.89  feet  square,  and  that  the  W1  column 
is  2  feet  X  2.78  feet.  This  means  that  the  net  average  load  is 
500  pounds  per  square  inch  on  each  column.  In  Fig.  31  let  ab 
equal  n,  and  cd  equal  m,  both  still  unknown.  The  smaller 
column  is  on  the  edge  of  the  property,  and  the  ab  line  is  made 
1.0  foot  from  the  column  center.  As  a  trial  solution,  assume 
that  the  cd  line  is  4.0  feet  beyond  the  other  column  center. 
Then  the  total  length  of  the  trapezoid  is  21.0,  and 

$  (m  +  n]  21.0  =  151.515 
(m  +  n)  =    14.43 

The  center  of  gravity  of  the  two  loads  is  at  ,  nnn  QAA  of  16 
feet,  or  at  9.6  feet  from  the  smaller  column  center.  This 
locates  0.  To  fulfil  condition  (2),  the  dimensions  m  and  n 
must  be  such  that  the  center  of  gravity  of  the  trapezoid  shall 
be  at  0.  In  general,  the  distance  z  of  the  center  of  gravity  of 
a  trapezoid  from  its  larger  base  equals  one-third  of  the  height 
1i  times  the  quotient  of  the  larger  base  plus  twu  e  the  smaller 
base  divided  by  the  sum  of  the  bases;  or,  as  an  equation 


Substituting  #  =  10.4,  h  —  21.0,  m  and  n  being  still  unknown, 

1'0*"1*2 

77~*~  A  -  j  - 

3          m  +  n 


114  REINFORCED  CONCRETE 

Combining  this  equation  with  the  equation  (m  +  n)  =  14.43, 
we  may  solve  and  find  m  =  7.419  and  n  =  7.011.  By  propor- 
tion, we  find  the  dimension  ef  through  0  =  7.217  feet. 

The  maximum  moment  is  found  where  the  shear  is  zero,  and 
this  must  be  at  the  right-hand  end  of  a  portion  of  the  slab  on 
which  the  net  upward  pressure  equals  600,000  pounds.  That 
portion  must  have  an  area  of  600,000  -*-  6,600  =  90.909  square 
feet.  Similarly,  the  remaining  area  is  computed  to  be  60.606 
square  feet.  Let  p  equal  the  length  of  this  section  (qs  in  the 
figure)  and  h  equal  its  distance  from  cd.  We  may  write  the 
two  equations 

|  (7.419  +  p)Ji  =  90.909 
and 

$(p  +  7.011)  (21  —  /?)  =  60.606 

Solving  these  two  equations  for  p  and  h,  we  have  p  =  7.178 
and  h  =  12.456.  It  should  be  noted  that  this  section  of  maxi- 
mum moment  (on  the  line  qs)  is  not  on  the  line  of  center  of 
gravity  of  the  whole  footing,  but  is  in  this  case  about  two  feet 
to  the  right.  The  center  of  gravity  of  the  trapezoid  cdqs, 
calculated  as  above,  is  at  a  point  6.262  feet  from  qs  and  the 
net  upward  pressure  on  this  section  is  600,000  pounds.  There- 
fore, taking  moments  about  qs,  we  have 

M  =  600,000  (8.456  -  6.262)  =  1,316,400  ft.-lb. 

=  15,796,800  in.-lb. 

In  this  case,  b  =  7.178  feet  =  86.136  inches ;  call  it  even  86. 
Then  for  M  =  95  bd2,  we  have 

95  bd2  =  8,170  d2  =  15,796,800 
d2  =  1,934 
d  =44.0  in. 
Then 

A  =  .00675  X  86X44  =  25.54  sq.  in. 

which  may  be  provided  by  20  bars,  1|  inches  square. 

That  portion  of  the  slab  between  x  and  z  is  subject  to  trans- 
verse stress,  the  parts  near  x  and  z  tending  to  bend  upward. 
Although  the  stresses  are  not  computable  with  perfect  definite- 


REINFORCED  CONCRETE  115 

ness,  being  comparable  to  those  in  a  simple  footing  (see  page 
104),  we  may  consider  them  as  approximately  measured  by  the 
moment  of  the  quadrilateral  between  the  face  of  the  column 
and  x  about  the  face  of  the  column,  xz  equals  7.34;  subtract- 
ing the  column  width  and  dividing  by  2  we  have  2.225  feet,  or 
26.7  inches;  the  area  of  the  quadrilateral  is  approximately 
i  (8  +  2.89)  2.225  =  12.11  square  feet.  The  effective  upward 
pressure  is  12.11  X  6,600  =  79,926  pounds.  The  lever  arm  is 
approximately  T6^  of  the  distance  from  the  face,  or  0.6  X  26.7  = 
16  inches. 

M  =  79,926  X  16  =  1,278,816  =  95  bd2 

Here  d  is  about  one  inch  less  than  for  the  main  slab,  or,  say, 
43  inches.  Solving,  b  =  7.3  and 

A  =  pbd  =  .00675  X  43  X  7.3  =  2.12  sq.  in. 

which  may  be  supplied  by  4  bars  f  inch  square.  This  calcula- 
tion shows  that  a  relatively  small  amount  of  reinforcement, 
which  should  run  under  the  column  from  x  to  z,  will  resist  this 
stress.  Increasing  the  number  of  bars  to  5  or  6  will  certainly 
cover  all  uncertainties  in  this  part  of  the  calculation.  The 
stresses  under  the  other  column  are  somewhat  less  and  there- 
fore the  same  reinforcement  will  be  even  safer. 

The  shear  around  the  larger  column  can  be  calculated  as 
"punching"  shear;  b  for  this  case  is  the  perimeter  of  the 
column,  and  equals  4X2.89  =  11.56  feet,  or  138.72  inches; 
jd  equals  .88X44  =  38.72;  V  equals  600,000  —  (2.892  X 
6,600)  =544,890. 

v  =  V  •*•  bjd  =  544,890  •*•  (138.72  X  38.72) 
=  102  Ib.  per  sq.  in. 

Since  this  is  a  case  of  true  shear,  when  a  working  stress  of 
120  pounds  per  square  inch  is  allowable,  no  added  reinforce- 
ment is  necessary. 

The  other  column  may  be  considered  similarly,  except  that 
it  is  supported  only  on  three  sides,  b  =  81  inches  and  bjd  = 
3,136;  7  =  300,000  —  36,667  =  263,333;  then  v  =  84.  Since 


116  REINFORCED  CONCRETE 

this  is  only  70  per  cent  of  the  allowable  stress  for  true  shear, 
it  is  probably  safe.  In  addition,  the  bending  down  of  the 
main  reinforcing-  bars  under  each  column,  as  shown  in  the 
figure,  will  add  a  very  large  factor  of  safety. 

It  is  far  more  difficult,  in  case  the  heavier  column  is  next  to 
the  property  line,  to  obtain,  by  the  analytical  method  given 
above,  a  trapezoid  which  will  fulfil  the  two  fundamental 
requirements  there  given.  If  the  wall  column  has  twice  (or 
more  than  twice)  the  lead  carried  by  the  inner  column,  no 
trapezoid  is  obtainable.  L:  such  a  case,  a  figure  shaped  some- 
what like  a  shovel,  the  blade  being  under  the  heavy  column 
and  the  handle  being  a  beam  which  transfers  the  load  of  the 
lighter  column  to  the  broad  base,  may  be  used,  the  dimensions 
and  exact  shape  of  which  can  only  be  determined  by  successive 
trials. 

PILES 

Advantage  of  Concrete  and  Reinforced  Concrete  Piles  A 
reinforced  concrete  pile  foundation  does  not  differ  essential!  v 
in  construction  from  a  timber  pile  foundation.  The  piles  art 
driven  and  capped,  in  the  usual  manner,  with  concrete  ready 
for  the  superstructure.  Compared  with  timber  piles,  rein- 
forced concrete  piles  have  the  advantage  of  being'  equally 
durable  in  a  wet  or  dry  soil,  and  the  disadvantage  of  being 
more  expensive  in  first  cost.  Sometimes  their  use  will  effect 
a  saving  in  the  total  cost  of  the  foundation  by  obviating  the 
necessity  of  cutting  the  piles  off  below  the  water  line.  The 
depth  of  the  excavation  and  the  volume  of  masonry  may  be 
greatly  reduced,  as  illustrated  in  Fig.  32.  This  figure  shows  a 
comparison  of  the  relative  amounts  of  excavation  which  would 
be  necessary,  and  also  of  the  concrete  which  would  be  required 
for  the  piles,  thus  indicating  the  economy  which  is  possible  in 
these  two  items.  There  is  also  shown  a  possible  economy  in 
the  number  of  piles  required,  since  concrete  piles  can  readily 
be  made  of  any  desired  diameter,  while  there  is  a  practical 
limitation  to  the  diameter  of  wooden  piles.  Therefore  a  smaller 
number  of  concrete  piles  will  furnish  the  same  resistance  as  a 
larger  number  of  wooden  piles.  In  Fig.  32  it  is  assumed  that 


REINFORCED  CONCRETE 


117 


the  three  concrete  piles  not  only  take  the  place  of  the  four 
wooden  piles  in  the  width  of  the  foundation,  but  that  there 
will  also  be  a  corresponding  reduction  in  the  number  of  piles 
in  a  direction  perpendicular  to  the  section  shown.  The  extent 
of  these  advantages  depends  very  greatly  on  the  level  of  the 
ground-water  line.  When  this  level  is  considerably  below  the 
surface  of  the  ground,  the  excavation  and  the  amount  of  con- 
crete required,  in  order  that  the  timber  grillage  and  the  tops 


SURFACE* 


Fig.  32.   Comparison  of  Wooden  and  Concrete  Piles 

of  the  piles  shall  always  be  below  the  water  line,  will  be  corre- 
spondingly great,  and  the  possible  economy  of  concrete  piles 
will  also  be  correspondingly  great, 

Capping  and  Driving.  The  pile  and  cap,  being  of  the 
same  material,  readily  bond  together  and  form  a  monolithic 
structure.  The  capping  should  be  thoroughly  reinforced  with 
steel.  Reinforced  concrete  piles  can  be  driven  in  almost  any 
soil  that  a  timber  pile  can  penetrate,  and  they  are  driven  in 
the  same  manner  as  the  timber  piles.  A  combination  of  the 
hammer  and  water  jet  has  been  found  to  be  the  most  successful 


118 


REINFORCED  CONCRETE 


manner  of  driving  them.  The  hammer  should  be  heavy  and 
drop  a  short  distance  with  rapid  blows,  rather  than  a  light  one 
dropping  a  greater  distance.  For  protection  while  being 
driven,  a  hollow  cast-iron  cap  filled  with  sand  is  placed  on  the 
head  of  the  pile.  The  cap  shown  in  Fig.  33  has  been  used 
successfully  in  driving  concrete  piles.  A  hammer  weighing  2,500 

pounds  was  dropped  25 
feet,  20  to  30  times  per 
minute,  without  injury 
to  the  head. 

Design.  There  is  no 
definite  way  to  figure 
the  size  or  length  of  a 
pile  to  support  a  given 
load.  Some  engineers 
have  determined  the  size 
of  the  piles  required  for 
their  work  by  assuming 
the  friction  between  the 
soil  and  concrete  to  be 
a  given  amount  per 
square  foot,  and  then 

,  ur  nuoc.  i ig5S2|E3g3s||     making  the  pile  of  suf- 
1]==-  =  ^  =  .;  ^^nPn^p"^       ficient  diameter  and 
i*JC|Fff&--  \WF£m&bss^     length  so  that  it  will  be 

safely  supported  by  this 
f rictional  area ;  others 
allow  300  to  500  pounds 
per  square  inch  of  the 


*2  "JET  PIPE 
ELEVATION 


SECTION 


Fig.  33.   Cushion  Head  for  Driving  Piles 

average  cross  section.  Where  it  is  possible,  it  is  far  better  to 
drive  the  pile  through  the  soft  material  and  a  short  distance 
into  a  firm  soil  than  to  depend  altogether  on  the  frictional 
resistance.  Borings  should  always  be  made  at  the  site  of  the 
work  to  ascertain  the  nature  of  the  material  and,  in  case  a  firm 
stratum  is  not  found  within  a  reasonable  depth,  a  few  piles 
should  be  made,  driven,  and  tested  as  to  their  safe  supporting 
capacity  before  any  definite  dimensions  are  assumed. 


REINFORCED  CONCRETE 


119 


SECTION  01 

? 

a 

\ 

1  ; 

PL  /7/V 


Concrete  piles  that  are  reinforced  with  steel  bars  will  resist 
lateral  blows  much  better  than  those  that  are  not  reinforced. 
Piles  that  are  made  and 
driven  must  be  rein- 
forced so  that  they  can 
be  handled  without 
breaking.  Four  bars  1 
inch  in  diameter,  with 
!-inch  bands  12  inches 
on  centers,  will  be  suffi- 
cient reinlorcement  for 
piles  14  to  16  inches  in 
diameter. 

Loading.  A  concrete 
pile  16  to  18  inches  at 
the  top,  tapering  to  8  or 
10  inches,  and  16  to  20 
feet  long,  should  safely 
support  a  load  of  20 
tons  in  fairly  soft,  wet 
soil,  and  25  to  30  tons 
when  driven  through  a 
soft  soil  into  a  firm  one. 
These  piles  cannot  be 
placed  closer  than  3  feet 
on  centers. 

Types.  Concrete  and 
reinforced  concrete  piles 
may  be  classified  under 
two  headings:  (a)  those 
which  are  formed,  har- 
dened, and  driven  very 
much  as  any  pile  is  driv- 
en; (b)  those  formed  by 


making    a   hole    in    the 


(*} 

Fig.  34. 


(*} 

Reinforced  Concrete  Piles 


ground,  ramming  in  the  concrete,  and  letting  it  harden. 

Reinforced  concrete  piles  which  have  been  formed  on  the 


120 


REINFORCED  CONCRETE 


ground  are  designed  as  columns  with  vertical  reinforcement 
connected  at  intervals  with  horizontal  bands.  These  piles  are 
usually  round  or  octagonal,  with  steel  or  cast-iron  points. 

Fig.  34-a  shows  a  type  commonly  used 
when  the  piles  are  constructed  in  forms, 
and  hardened,  and  driven  just  as  a  wooden 
pile.  The'se  piles  must  be  reinforced  with 
steel  so  that  they  can  be  handled. 

Fig.  34-fr  shows  the  general  plan  of  a 
type  of  pile  that  has  been  used  to  some 
extent  along  the  seashore  where  piles  can 
be  jettied.  They  are  usually  molded  in  a 
vertical  position  and  as  soon  as  they  can 
be  handled  are  jettied  in  place.  These  piles 
are  not  dependent  on 


the  friction  of  the  sur- 
face of  the  concrete 
with  the  sand  but  can 
convey  the  load  directly 
to  the  sand  under  the 
enlarged  end.  Piles  of 
this  type  have  been  used 
for  loads  of  50  to  60 
tons.  They  cannot  be 
used  in  clusters,  but 
each  pile  must  be  of 
sufficient  size  to  support 
the  entire  load  at  any 
given  point. 

Raymond  Concrete 
Pile.  The  Raymond  con- 
crete pile,  Fig.  35,  is 
constructed  in  place.  A 
collapsible  steel  pile  core 
is  encased  in  a  thin,  closely  fitting,  sheet-steel  shell.  The  core 
and  shell  are  driven  to  the  required  depth  by  means  of  a  pile 
driver.  The  core  is  so  constructed  that  when  the  driving  is 


Fig.  35.    Raymond  Concrete  Pile 


REINFORCED  CONCRETE 


121 


finished,  it  is  collapsed  and  withdrawn,  leaving  the  shell  in  the 
ground,  which  acts  as  a  mold  for  the  concrete.  When  the  core 
is  withdrawn,  the  shell  is  filled  with  concrete,  which  is  tamped 
during  the  filling  process.  These  piles  are  usually  from  18  to 
20  inches  in  diameter  at  the  top,  and  from  6  to  8  inches  at  the 
point.  When  it  is  desirable,  the  pile  can  be  made  larger  at 


CftST  IKON  POINT  DRIVINQ  FORM. 
OPERATION  FINISHED  PIU 


flLLICjflTOK  POINT  DRIVIWf  FOKM. 

OPERATION  FINISHED  PILE 


(")  (*) 

Fig.  36.    Standard  Simplex  Concrete  Piles 

the  small  end.  The  sheet  steel  used  for  these  piles  is  usually 
No.  20  gage.  When  it  is  desirable  to  reinforce  these  piles,  the 
bars  are  inserted  in  the  shell  after  the  core  has  been  withdrawn 
and  before  the  concrete  is  placed. 

Simplex  Concrete  Pile.  The  different  methods  for  produc- 
ing the  Simplex  pile  cover  the  two  general  classifications  of 
concrete  piles— namely,  those  molded  in  place,  and  those  molded 


122 


REINFORCED  CONCRETE 


above  ground  and  driven  with  a  pile  driver.  Fig.  36  shows  the 
standard  methods  of  producing  the  Simplex  pile:  A  shows  a 
cast-iron  point  which  has  been  driven  and  imbedded  in  the 
ground,  the  concrete  deposited,  and  the  form  partially  with- 
drawn; while  B  shows  the  alligator-point  driving  form.  The 
only  difference  between  the  two  forms  shown  in  this  figure  is 
that  the  alligator  point  is  withdrawn  and  the  cast-iron  point 
remains  in  the  ground.  The  concrete  in  either  type  is  com- 
pacted by  its  own  weight.  As  the  form  is  removed,  the  con- 


Fig.   37.     Types  of  Foundation  for  Boston  and  Maine  Railroad 

crete  comes  in  contact  with  the  soil  and  is  bonded  with  it.  There 
is  the  danger  in  using  this  type  of  pile  that,  if  a  stream  of 
water  is  encountered,  the  cement  may  be  washed  out  of  the 
concrete  before  it  has  a  chance  to  set. 

A  shell  pile  and  a  molded  and  driven  pile  are  also  produced 
by  the  same  company  which  manufactures  the  Simplex,  and 
are  recommended  for  use  under  certain  conditions.  Any  of 
these  types  of  piles  can  be  reinforced  with  steel.  This  com- 
pany has  driven  piles  20  inches  in  diameter  and  75  feet  long. 

Cost.  Concrete  or  reinforced  piles  will  cost  much  more 
per  lineal  foot  than  wood  piles,  but  will  support  greater  loads, 


REINFORCED  CONCRETE  123 

and  therefore  fewer  piles  are  required.  As  already  shown  in 
Fig.  32,  it  is  often  more  economical  to  use  concrete  piles  than 
wood  piles.  Concrete  piles  have  been  driven  for  $0.70  per 
lineal  foot,  but  the  average  price  is  probably  $0.90  to  $1.00. 
The  Boston  and  Maine  Railroad  has  recently  completed  the 
erection  of  a  large  group  of  shop  buildings  at  Billerica,  Massa- 
chusetts, in  which  about  3,000  concrete  piles  were  used.  These 
buildings  were  all  supported  on  concrete  piles,  as  the  soil 
consists  of  sand  and  peat  on  the  surface  and  is  underlaid  by 
water-bearing  sand.  Fig.  37  shows  the  three  designs  con-> 
sidered,  which  were  as  follows: 

(1)  Concrete  piers  carried  down  in  open  caissons  to  firm 
strata ;   loading  per  square  foot,  3.2  tons. 

(2)  Wooden   piles  cut   off  below  ground-water  level  and 
capped  with  concrete  piers ;  loading  per  pile,  15  tons. 

(3)  Concrete  piles  driven  from  the  surface  of  the  ground 
and  capped  with  reinforced  concrete ;  loading  per  pile,  30  tons. 

The  estimates  for  these  different  types  of  foundations  .were 
as  follows:  CONCRETE  PIERS  * 

Excavation,  pumping,  and  backfill $  90.00 

Sheeting  and  bracing < .      100.00 

Concrete,  18.5  cu.  yds.,  at  $7.50 ; 138.75 

Total  cost $328.75 

WOODEN  TILE  PIER 

Excavation,  pumping,  and  backfill $  40.00 

Sheeting  and  bracing 60.00 

Concrete,  17.5  cu.  yds.  at  $7.50 131.25 

16  wooden  piles  at  $5,00 80.00 

Total  cos't $311.25 

CONCRETE  PILE  PIER 
Reinforced   concrete  cap    (including  excavation),  6|   cu.  yds. 

at  $9.00 - $  60.00 

8  concrete  pedestal  piles  at  $15.00 120.00 

Total  cost •» , $180.00 

RETAINING  WALLS 

Properties  of  Supported  Material  Affect  Design.    A  retain- 
ing wall  is  a  wall  built  to  sustain  the  lateral  pressure  of 
*  Concrete-Cement  Age,  October,  1914. 


124  REINFORCED  CONCRETE 

earth.  The  pressure  that  will  be  exerted  on  the  wall  will  de- 
pend on  the  kind  of  material  to  be  supported,  the  manner  of 
placing  it,  and  the  amount  of  moisture  that  it  contains.  Earth 
and  most  other  granular  masses  possess  some  frictional  sta- 
bility. Loose  soil  or  a  hydraulic  pressure  will  exert  a  full 
pressure;  but  a  compacted  earth,  such  as  clay,  may  exert  only 
a  small  pressure  due  to  the  cohesion  in  the  materials.  This 
cohesion  cannot  be  depended  upon  to  relieve  the  pressure 
against  a  wall,  for  the  cohesion  may  be  destroyed  by  vibration 
due  to  moving  loads  or  to  saturation.  In  designing  a  wall  the 
pressure  due  to  a  granular  or  a  semifluid  mass  without  cohesion 
must  always  be  considered. 

Failures  of  Walls.  There  are  three  ways  in  which  a 
masonry  wall  may  fail:  (1)  by  sliding  along  a  horizontal 
plane;  (2)  by  overturning  or  rotating;  (3)  by  the  crushing 
of  the  masonry  or  its  footing.  These  are  the  points  that  must 
be  considered  in  order  to  design  a  wall  that  will  be  successful 
in  resisting  an  embankment.  A  wall,  therefore,  must  be  of 
sufficient  size  and  weight,  to  prevent  the  occurrence  of  sliding, 
rotation,  or  crushing. 

Stability  of  Wall  against  Sliding.  Stability  against  sliding 
is  secured  by  making  the  structure  of  sufficient  weight  so  that 
there  will  be  no  danger  of  a  movement  at  the  base.  In  Fig.  38 
let  E  be  the  horizontal  pressure  and  assume  W  to  be  the  weight 
of  all  materials  above  the  joint.  A  movement  will  occur  when 
E  =  fW,  where  /  is  the  coefficient  of  friction.  Let  n  be  a 
number  greater  than  unity,  the  factor  of  safety;  then  in  order 
that  there  be  no  movement  n  must  be  sufficiently  large  so  that 
nE  =  fW.  A  common  value  for  n  is  2,  but  sometimes  it  is 
taken  as  low  as  1£.  Substituting  2  for  n, 
2E  =  fW 
^~  (20) 

An  average  value  of  the  coefficient  of  friction  for  masonry 
on  masonry  is  0.65;  for  masonry  on  dry  clay,  0.50;  for  ma- 
sonry on  wet  clay,  0.33;  for  masonry  on  gravel,  0.60;  for 
masonry  on  wood,  0.50. 


REINFORCED  CONCRETE 


125 


Stability  of  Wall  against  Rotation.  The  stability  of  a  wall 
against  rotation  is  secured  by  making  the  wall  of  such  dimen- 
sion and  weight  that  the  resultant  R  of  the  external  forces  will 
pass  through  the  base  and  well  within  the  base,  as  shown  in 
Fig.  38.  Generally,  in  designing,  the  resultant  is  made  to 
come  within  or  at  the  edge  of  the  middle  third.  The  nearer  the 
center  of  the  base  the  resultant  comes,  the  more  evenly  the 
pressure  will  be  distributed  over  the  foundation  for  the  wall. 
When  R  passes  through  A,  Fig.  38,  the  wall  will  fail  by  rota- 
tion. Methods  for  finding  R  will  be  demonstrated  in  another 
paragraph. 

Stability  of  Wall  against  Crushing.  The  compressive  unit 
stresses  in  walls  built  on  stone  foundations  must  not  be 
greater  than  the  unit  stresses  per- 
mitted for  safe  working  loads  of 
masonry;  but  when  a  wall  is 
built  on  clay,  sand,  or  gravel,  the 
allowable  pressure  for  such  foun- 
dations must  not  be  exceeded. 

Foundations  for  Wall.  The 
foundations  for  a  retaining  wall 
must  be  below  the  frost  line, 
which  is  about  three  feet  below 
the  surface  in  a  temperate  cli- 
mate, and  deeper  in  a  cold 
climate.  The  foundation  should 
be  of  such  a  character  that  it 
will  safely  support  the  wall.  If  necessary,  the  soil  should  be 
tested  to  determine  if  it  will  safely  support  the  wall. 

The  foundation  should  always  be  well  drained.  Many  fail- 
ures of  walls  have  occurred  owing  to  the  lack  of  drainage. 
Water  behind  a  wall  greatly  increases  the  stresses  in  the  wall. 
Water  freezing  behind  a  wall  usually  causes  it  to  bulge  out, 
the  first  step  in  the  failure  of  the  wall.  On  a  clay  foundation 
the  friction  is  greatly  reduced  by  the  clay  becoming  thoroughly 
soaked  with  water.  It  has  just  been  shown  that  the  difference 
of  the  coefficients  of  friction  of  masonry  on  dry  clay  and  wet 


Pig.  38.    Section  of  Retain- 
ing Wall 


126  REINFORCED  CONCRETE 

cl^ay  is  0.17.  There  are  different  ways  of  draining  a  fill  behind 
a  retaining-  wall.  Pipes  2  to  4  inches  in  diameter  are  often  built 
in  the  wall,  as  shown  in  Fig.  38. 

Fill  behind  Wall.  The  fill  behind  the  wall  is  sometimes 
made  horizontal  with  the  top  of  the  wall;  at  other  times  the 
fill  is  sloped  back  from  the  top  of  the  wall,  as  shown  in  Fig. 
38.  When  there  is  a  slope  to  be  supported,  the  wall  is  said 
to  be  surcharged,  and  the  load  to  be  supported  is  greater  than 
for  a  horizontal  fill. 

Design  of  Wall 

Methods  of  Designing  Walls.  In  designing  a  retaining 
wall  the  dimensions  of  the  section  of  a  wall  are  generally 
assumed  and  then  the  section  investigated  graphically  to  see  if 
the  assumed  conditions  are  met.  There  are  theoretical  lor- 
mulas  for  designing  walls  which  will  be  given.  In  designing 
a  wall,  the  student  is  advised  to  make  first  the  section  accord- 
ing to  the  formulas  and  then  to  investigate  it  graphically.  All 
existing  walls  in  that  vicinity  should  be  examined  to  determine 
their  dimensions  and  to  discover  if  they  have  been  successfully 
designed.  Often,  existing  walls  will  give  more  information  to 
an  engineer  than  he  will  obtain  by  a  theoretical  or  graphical 
study. 

In  recent  years  concrete  has  come  into  extensive  use  in 
building  retaining  walls.  A  wall  built  of  a  1:3:6  concrete 
should  be  equal  in  strength  to  a  wall  built  of  cut  stone  or 
large-ranged  rubble.  In  heavy  walls  large  stones,  25  to  50  per 
cent  of  the  volume,  are  often  placed  in  the  concrete.  This, 
usually,  greatly  reduces  the  cost  of  the  wall  and  does  not  weaken 
the  wall  if  the  stones  are  properly  placed. 

Face  of  Wall.  The  front  or  face  of  a  retaining  wall  is 
usually  built  with  a  batter.  This  batter  often  varies  from  less 
than  an  inch  per  foot  in  height  to  more  than  an  inch  per  foot. 
The  rear  face  may  be  built  either  straight,  with  a  batter,  or 
stepped  up.  A  wall  should  never  be  less  than  2£  feet  to  3 
feet  wide' on  top,  unless  it  is  a  very  small  one.  In  that  case, 
probably  a  width  of  12  to  18  inches  would  be  sufficient. 


REINFORCED  CONCRETE  127 

Width  of  Base.  The  width  of  the  base  of  a  concrete 
gravity  wall  varies  from  35  per  cent  to  50  per  cent  of  the 
height  of  the  wall.  Probably  the  majority  of  walls  are  con- 
structed with  a  width  of  base  of  about  45  per  cent  of  the 
height.  For  railroad  work  this  dimension  is  sometimes  made 
greater  than  50  per  cent,  ranging  up  to  60  per  cent. 

Pressure  behind  Wall.  The  development  of  the  formulas 
for  finding  the  pressure  behind  a  wall  is  a  long,  complicated 
theory,  and  the  demonstration  will  not  be  given  here.  The 
formulas  given  are  those  usually  found  in  textbooks.  They 
are  based  on  the  Rankine  theory,  which  considers  that  the  earth 
is  a  granular  mass  with  an  assumed  angle  of  repose  of  1.5  to  1, 
which  in  degrees  is  33°  42'.  In  applying  this  method  it  is 
immaterial  whether  the  forces  representing  the  earth  pressure 
are  considered  as  acting  directly  upon  the  -back  of  the  wall, 
or  are  considered  as  acting  on  a  vertical  plane  passing  through 
the  extreme  back  of  the  footing.  In  the  latter  case,  the  force 
representing  the  lateral  earth  pressure  must  be  combined  (1) 
with  the  vertical  force  representing  the  weight  of  the  earth 
prism  between  the  back  of  the  wall  and  the  vertical  plane  con- 
sidered; and  (2)  with  the  vertical  force  representing  the 
weight  of  the  wall  itself. 

In  the  formulas*  for  determining  pressures  behind  a  wall,  let 
E  equal  total  pressure  against  rear  face  of  wall  on  a  unit 
length  of  wall ;  W  equal  weight  of  a  unit  volume  of  the  earth ; 
h  equal  height  of  wall;  and  <£  equal  angle  of  repose. 

When  the  upper  surface  of  the  earth  is  horizontal,  the 
equation  is 

0      ^\  W  h2 
~2J  —  (21) 

Since  the  angle  of  repose  for  the  earth  behind  the  wall  has 
been  taken  as  33°  42',  equation  (21)  may  be  reduced  to  the 
following  form  by  substituting  the  value  of  the  tangent  of  the 
angle  in  the  equation 

E  =  .2SG^-2  (21a) 


128 


REINFORCED  CONCRETE 


When  a  wall  must  sustain  a  surcharge  at  the  slope  of  1.5  to  1, 
the  equation  is 

E  =  %cos<f>Wh*  (21b) 

or 

IV  Ti'J 


=  .833 


a 


(21c) 


The  force  E  is  applied  at  one-third  the  height  of  the  wall, 
measured  from  the  bottom,  but  for  a  surcharged  wall  it  is 
applied  at  one-third  of  the  height  of  a  plane  that  passes  just 


(a) 


Fig.  39.    Diagrams  Showing  Pressures  on  Foundations 

behind  the  wall.     This  is  clearly  shown  in  the  different  figures 
illustrating  retaining  walls. 

The  direction  of  the  center  of  pressure  E  is  assumed  as 
being  parallel  to  the  top  of  the  earth  back  of  the  wall.  The 
angle  of  the  surcharge  is  generally  made  1.5  to  1. 

Example.  What  is  the  pressure  per  foot  of  length  of  a  wall  18  feet 
high,  earth  weighing  100  pounds  per  cubic  foot,  if  the  fill  is  level  with 
the  top  of  the  wall? 

Solution.    Substituting  in  Equation  (21a) 


,280^ 


:.286 


100  X  18a 


4,633  Ib. 


REINFORCED  CONCRETE  129 

Pressure  on  Foundation.  The  formulas  given  below  for 
determining  the  pressure  on  the  foundation  are  the  ones  rec- 
ommended to  the  American.  Railway  Engineering  Association 
by  a  committee  appointed  by  that  Society  to  investigate  the 
subject  of  retaining  walls.  (See  Fig.  39.) 

NOTE.  —  When  P  equals  the  vertical  component  of  the  resultant  pres- 
sure on  the  base,  B  is  the  full  width  of  the  base  in  feet,  and  Q  is  the 
distance  from  the  toe  to  where  the  force  P  cuts  the  base. 

When  Q  is  equal  to  or  greater  than  — 

o 

P 

Pressure  at  the  toe  =  (4  B  —  6  Q  )  —^        (21d) 

ZJ 

p 

Pressure  at  the  heel  =  (6  Q  —  2  B)  ^r        (21«) 

B 

When  Q  is  less  than  ^ 

2  P 

Pressure  at  the  toe  =  (21f  ) 


Illustrative  Example.  A  retaining  wall  is  to  be  designed  to 
support  an  embankment  18  feet  high,  the  top  of  the  fill  being 
level  with  the  top  of  the  wall,  the  face  of  the  wall  to  be  vertical, 
the  back  to  slope. 

Draw  an  outline  ,of  the  proposed  section,  Fig.  40,  and  then 
investigate  the  section  to  see  if  it  has  sufficient  strength  to 
support  the  .embankment.  Make  the  base  45  of  the  height  of 
the  wall. 

Width  of  base  =  18  X  .45  =  8.1  feet 

Assume  the  width  at  the  top  to  be  2  feet  and  find  the  pres- 
sure E  at  the  back,  substituting  in  Equation  (21a),  and  apply 

TT 

that  pressure  at  —  — 
o 


.  . 

P  is  found  by  dividing  the  wall  into  rectangles  and  a  triangle 


130 


REINFORCED  CONCRETE 


and  determining  the  weights  and  the  center  of  gravity  of  each, 
and  also  of  the  earth  back  of  the  wall,  and  then  finding  the 
combined  weights  and  the  center  of  gravity  of  the  wall  and 
earth.  Assume  that  the  weight  of  the  masonry  is  150  pounds 
per  cubic  foot  and  the  earth  100  pounds  per  cubic  foot,  and 
consider  the  section  of  wall  as  being  one  foot  in  length.  The 
details  of  the  computation  are  given  below: 

Center  of  Gravity  of  Wall 

(Moments  taken  about  A) 


SECTIONS 

AREA 
(Sq.  Ft.) 

MOMENT 
Aim 

MOMENT 
AREA 

a  b  c  d 
t'fgh 
h  ig 

24.3 
30.0 
27.0 

4.05 
2.00 
4.20 

98.4 
60.0 
113.4 

81.3 

271.8 

Distance  from  A  to  center  of  gravity  =  271.8  -*•  81.3  =  3.34  ft. 
Weight  of  wall  per  lineal  foot  =  81.3  X  150  =  12,195  Ib. 
Static  moment  about  A  =  12,195  X  3.34  =  40,730  ft.-lb. 

Center  of  Gravity  of  Earth 

(Moments  taken  about  A) 


SECTION 

AREA 
(Sq.  Ft.) 

MOMENT 
ARM 

MOMENT 
AREA 

i}g 
ijkc 

27.0 
22.5 

49.5 

5.4 
7.35 

145.8 
1G5.4 

311.2 

Distance  from  A  to  center  of  gravity  =  311.2  -*•  49.5  =  0.3  ft. 
Weight  of  earth  per  lineal  foot  =  49.5  X  100  =  4,950  Ib. 
Static  moment  about  A  =  4,950  X  6.3  =  31,185  ft.-lb. 

The  position  of  the  resultant  is  determined  by  dividing  the 
sum  of  the  static  moments  by  the  sum  of  the  weights: 
40,730  +  31,185  _  71,915  _ 
12,195+    4,950       17,145 

Produce  E  to  meet  the  vertical  line  passing  through  the  com- 
bined centers  of  gravity.  On  this  vertical  line  lay  off  the  value 
of  P,  which  is  17,145  pounds,  to  any  convenient  scale.  At  the 


REINFORCED  CONCRETE 


131 


lower  end  of  P  draw  a  line  parallel  to  line  E  and  on  this  line 
lay  off  the  value  of  E,  which  is  4,633.     Draw  line  mn,-  which 


z'o 


Fig.  40.     Design  Diagram   for   Simple   Retaining  Wall 

is  the  resultant  of  the  two  forces.     This  line  cuts  the  base  at 
a  scaled  distance  of  2.6  feet  from  the  toe,  which  is  about  one 

inch  outside  the  middle  third ;  therefore  Q  is  less  than    -  • 

•  O 

Substituting  in  Equation  (21f)  for  the  condition  when  Q  is 

ID 

less  than  -= ,  we  have 

o 

2       17 145 
Pressure  at  toe  =     X  =  4>397 lb- 


132  REINFORCED  CONCRETE 

Lay  off  to  any  convenient  scale  the  weight  4,397  pounds,  and 
on  the  base  lay  off  a  distance  equal  to  3  Q  =  7.8  feet.  Through 
this  point  draw  Op  and  scale  the  force  shown  from  I  to  the 
base  line  b,  which  is  less  than  200  pounds  and  need  not  be 
further  considered. 

The  pressure  at  the  toe,  4,397  pounds,  is  easily  supported  on 
any  ordinary  soil  and  the  uplift  at  the  heel,  200  pounds,  is  too 
small  to  be  considered.  This  section  should  be  safe  for  the 
conditions  given  in  the  problem. 

Reinforced  Concrete  Walls.  These  are  usually  made  in 
such  shape  that  advantage  is  taken  of  the  weight  of  part  of 
the  material  supported  to  increase,  the 
stability  of  the  wall  against  overturn- 
ing. Fig.  41  shows  the  outline  of  such 
a  wall.  It  consists  of  a  vertical  wall 
C  D,  attached  to  a  floor  plate  A  B. 
To  prevent  the  wall  from  overturning, 
the  moment  of  downward  forces  about 
the  outer  edge  of  the  base  M^  =  WJ^ 
+  W212,  must  be  greater  than  that  of 
the  overturning  moment,  M2  =  Ely 
MI  should  be  from  one  and  one-half 
to  twice  l/2,  which  would  be  the  factor 
of  safety.  In  addition  to  this  factor  of 

Fig.  41.   Outline  of  Re-   safety  there  would  be  the  shearing  of 
inforced    Concrete   Wall  J 

the  earth  along  the  line  ab. 

Owing  to  the  skeleton  form  of  these  walls  it  is  usually  more 
economical  to  construct  them  than  solid  walls  of  masonry.  The 
cost  per  cubic  yard  of  reinforced  concrete  in  the  wall  will  be 
more  than  the  cost  per  cubic  yard  of  plain  concrete  or  stone, 
in  a  gravity  retaining  wall,  but  the  quantity  of  material  re- 
quired will  be  reduced  by  30  to  50  per  cent  in  most  cases. 
There  are  two  forms  of  these  walls.  The  outline  in  Fig.  41 
shown  in  solid  lines  is  the  simpler  to  construct  and  is  the  more 
economical  of  the  two  types  of  reinforced  concrete  walls,  up  to 
a  height  of  18  feet.  For  higher  walls  the  form  shown  by  the 
solid  lines  and  heavy  dotted  line  be  is  used. 


REINFORCED  CONCRETE 


133 


Illustrative  Example.  Suppose  a  retaining  wall  is  to  be 
designed  which  is  to  be  14  feet  high  to  support  an  earth  face 
with  a  surcharge  at  a  slope  of  1.5  to  1. 

The  width  of  the  base  for  reinforced  concrete  walls  is  usually 
made  from  .4  to  .6  of  the  height.  For  this  wall,  with  a  sur- 
charge, the  base  will  be  made  one-half  of  the  height,  14  X  £  =  7 
feet.  Assume  the  weight  of  the  earth  at  100  pounds  per  cubic 
foot  and  the  reinforced  concrete  at  150  pounds  per  cubic  foot. 


Fig.  42.    Design  Diagrams  for  Retaining  Wall 
Substituting  in  Equation  (21c),  we  have 


E  =  .833 


Wh2 


=  .833  X   - 


100  X  142 


=  8,163  Ib. 


This  force  is  applied  on  the  plane  cm,  Fig.  42,  at  a  point  one- 
third  of  the  height  above  the  base. 

It  will  be  necessary  to  determine  the  thickness  of  the  vertical 


134  REINFORCED  CONCRETE 

• 

wall  and  the  base  plate  before  the  stability  of  the  wall  can 
be  determined.  Assume  the  base  plate  to  be  18  inches  thick; 
then  the  vertical  slab  will  be  12  feet  6  inches  high  and  the 
pressure  against  this  slab  will  be 


E  =  .833-  '°  X212"5      =  6,508  Ib. 

The  horizontal  component  of  this  pressure  is  6,508  X  cos  33° 
42'  =  5,421  pounds,  as  shown  diagrammatically  in  Fig.  42. 
The  bending  moment  would  be 


M  =  5,421  X         -  X  12  =  271,050  in.-lb. 

Placing  this  value  of  M  equal  to  95  bd2  in  which  b  =  12,  and 
solving  for  d,  we  have 


95 

d2  =  238 
d  =15.4  in. 

With  2.6  inches  added  for  protecting  this  steel,  the  total 
thickness  would  be  18  inches.  The  area  of  the  reinforcing 
steel  would  be  .00675  X  15.4  =  .104  square  inch  of  steel  per 
inch  of  length  of  wall.  Bars  1|  inches  round  (.99  -*•  .10  =  9.9) 
spaced  10  inches  apart,  will  be  required.  The  bending  moment 
rapidly  decreases  from  the  bottom  of  the  slab  upwards,  and, 
therefore,  it  will  not  be  necessary  to  keep  the  thickness  of  18 
inches  to  the  top  of  the  slab  or  to  have  all  the  bars  the  full 
length.  Make  the  top  9  inches  thick  ;  drop  off  one-third  of  the 
bars  at  one-third  of  the  height  of  the  slab  and  one-third  at  two- 
thirds  of  the  height.  The  shear  at  the  bottom  of  the  slab  is 
5,421  •*-  (12  X  15.4)  =29  pounds  per  square  inch;  therefore, 
as  this  does  not  exceed  the  working  stress,  no  stirrups  are 
needed. 

It  is  very  important  in  a  wall  of  this  type  not  to  exceed  the 
bonding  stress.  The  vertical  bars  must  be  well  anchored  in  the 
base  plate  or  they  will  be  of  no  great  value.  Since  the  bars 
are  1|  inches  in  diameter,  the  circumference  is  3.53  inches.  If  a 
bonding  stress  of  75  pounds  per  square  inch  is  allowed  for,  the 


REINFORCED  CONCRETE 


135 


total  bonding  per  inch  of  length,  of  bar  is  3.53X75  =  265 
pounds.  The  lever  arm  is  15.4  inches.  As  the  bars  are  spaced  10 
inches  on  centers,  the  stress  to  be  resisted  is  f  of  271,050,  or 
225,875  inch-pounds.  Let  x  be  length  of  anchorage  required, 
then 

M  =  2G5  X  15.4  X  x  =  225,875 
x  =  55  in. 

That  is,  the  vertical  IJ-inch  round  bars  must  extend  into  the 
footing  55  inches  or  be  anchored  in  such  a  way  that  their 
strength  will  be  developed. 

In  designing  the  footing  of  a  reinforced  concrete  retaining 
wall  the  resultant  force  should  intersect  the  base  within  the 
middle  third,  as  in  a  masonry  wall.  The  forces  acting  on  the 
footing  are  the  earth  pressure  on  the  plane  me,  the  weight  of 
the  earth  fill,  and  the  weight  of  the  concrete.  The  distance 
from  the  toe  a  to  the  point  where  the  resultant  acts  is  obtained 
as  follows:  The  centers  of  gravity  of  the  concrete  and  the 
earth  are  found,  also  the  weight  of  each.  The  weights  are 
multiplied  by  the  distances  from  a,  respectively,  which  gives 
the  static  moment.  The  sum  of  the  static  moments  divided  by 
the  sum  of  the  weights  equals  the  distance  from  .the  toe  to  the 
line  at  which  the  resultant  acts.  The  detail  figures  for  the 
problem  are  given  below. 

Center  of  Gravity  of  Wall 

(Moments  taken  about  a) 


SECTIONS 

AREA 
(Sq.  Ft.) 

MOMENT 

A  KM 

MOMENT 
AREA 

a  T)  c  d 
cft-g 
f  ih 

10.50 
9.38 
4.69 

3.50 

1.88 
2.50 

36.75 
17.63 
11.73 

66.11 

24.57 

Distance    from    a    to    center    of    gravity  =  66.11  -*-  24.57  = 
2.69  ft. 

Weight  per  lineal  foot  =  24.57  X  150  =  3,686  =  Wc 
Static  moment  about  a  =  3,686  X  2.69  =  9,915  ft.-lb. 


136 


REINFORCED  CONCRETE 


Center  of  Gravity  of  Earth 

(Moments  taken  about  a) 


SECTIONS 

AREA 
(Sq.Ft.) 

MOMENT 
Au.u 

MOMENT 
AKEA 

/  k  h 
hi)  11; 
Jim 

4.69 

50.00 
7.50 

2.75 
5.00 
5.42 

12.90 
250.00 
40.65 

62.19 

303.55 

Distance  from  a  to  center  of  gravity  =  303.55  -*-  62.19  = 
4.88  ft. 

Weight  per  lineal  foot  =  62.19  X  100  =  6,219  =  \Ve 

Static  moment  about  a  =  6,219  X  4.88  =  30,355  f  t.-lb. 

The  distance  from  a  to  the  combined  center  of  gravity  of  the 
concrete  and  the  earth  fill  is 

9,915  +  30,355      _  40,270 
3,686  +    6,219    =       9,905  ~~ 

To  find  where  the  resultant  E  cuts  the  base,  produce  E  to 
meet  the  combined  center  of  gravity  of  the  concrete  and  earth. 
From  their  intersection  lay  off  on  the  vertical  line,  at  any 
convenient  scale,  the  combined  weight  9,905  pounds.  At  the 
end  of  this  distance  draw  a  line  parallel  to  the  line  E  and  lay 
off  the  value  of  E  which  is  8,163  pounds.  Draw  E,  which  is 
the  resultant  and  in  this  case  cuts  the  base  at  the  edge  of  the 
middle  third,  so  that  the  wall  will  not  fall  by  overturning. 

The  pressure  produced  on  the  foundation  is  next  to  be  in- 
vestigated. Since  the  resultant  comes  at  the  edge  of  the 
middle  third,  Equations  (21d)  and  (21e)  are  used. 

p 
Pressure  at  the  toe  =  (4 B  —  6  Q)  — r 

=  [(4X7)  —  (6  X2.33)] 

=  4,242  Ib. 

P 

Pressure  at  the  heel  =  (6  Q- —  2  B) -#r 

'  B  14  050 

=  [(6  X  2.33)  -  (2  X  7)]  Hp- 
=-0 


REINFORCED  CONCRETE  137 

The  pressure  on  the  foundation  of  4,242  pounds  at  the  top  is 
permissible  on  most  soils. 

The  stability  of  a  wall  of  this  type  must  be  carefully  inves- 
tigated. Suppose  this  wall  is  to  be  located  on  a  wet  clay  soil. 
The  coefficient  of  friction  between  concrete  and  wet  clay  is  .33. 
The  horizontal  force  is  6,800  pounds,  and  the  weight  of  the 
concrete  and  earth  acting  in  a  downward  direction  is  9,015 
pounds.  With  a  coefficient  of  .33  or  i,  the  resistance  to  sliding 
is  9,915  X  £  =  3,305  pounds,  which  is  less  than  one-half  of 
the  horizontal  pressure,  6,800.  The  resistance  should  be  about 
twice  the  pressure  in  order  to  make  the  wall  safe  against 
sliding,  and  this  would  require  that  the  weight  should  be  about 
four  times  as  much,  in  order  that  mere  friction  should  surely 
prevent  sliding.  This  shows  that  it  will  be  necessary  to  con- 
struct a  projection  in  the  base,  as  shown  in  Fig.  42. 

The  thickness  of  the  base  is  always  made  greater  than  the 
moment  requirements  just  behind  the  vertical  slab  (or  at  h) 
would  demand.  If  the  wall  were  actually  on  the  point  of 
tipping  over,  there  would  cease  to  be  any  upward  pressure  on 
the  base.  But  there  would  be  a  downward  pressure  on  the 
right  cantilever  equal  to  the  weight  of  the  earth  above  it,  and 
the  moment  in  the  base  at  the  point  h  would  be  that  produced 
by  that  earth  pressure  and  by  the  weight  of  the  concrete  from 
h  to  b.  Since  the  foregoing  calculations  for  the  stability  of 
the  wall  show  that  the  computed  lateral  pressure  cannot  pro- 
duce actual  tipping  about  the  toe,  no  such  moment  can  really 
be  developed,  but  the  calculation  of  the  required  thickness  to 
resist  such  a  moment  gives  a  dimension  which  is  certainly 
more  than  safe  and  which,  for  other  reasons,  is  sometimes  made 
still  greater.  The  weight  of  the  earth  is  6,219  pounds  and  the 
weight  of  the  concrete  is  4  X  If  X  150  =  900  pounds.  Then 
6,219  +  900  =  7,119  pounds.  Therefore 

M  =  7,119  X  1.90  X  12  =  162,313  in.-lb. 

Placing  this  moment  equal  to  M  =  95  bd2  and  solving  for  d, 
we  find  that  d  equals  11.9.  If  2.5  inches  are  added  for  pro- 
tecting the  steel,  the  total  thickness  would  be  14.4  inches.  To 


138  REINFORCED  CONCRETE 

anchor  properly  the  bars  in  the  vertical  slab  the  thickness  of 
base  plate  is  seldom  made  less  than  the  vertical  slab.  There- 
fore, we  will  make  d  =  15  inches,  b  =  12,  and  solve  for  the 
moment  factor  E. 

M  =  12  XI52XE  =  158,977 
E  =  58.8 

Fig.  20  shows  that  when  E  =  59,  then  c  =  400,  s  =  12,000, 
and  that  the  percentage  of  steel  required  is  practically  .000. 
The  steel  required,  therefore,  is  12  X  15  X  .006  =  1.08  square 
inches,  and  bars  1|  inches  in  diameter,  spaced  10  inches,  will 
be  needed.  The  moment  in  this  part  of  the  base  plate  is  nega- 
tive ;  therefore  the  steel  must  be  placed  in  the  top  of  the  concrete. 

The  vertical  shear  is  7,129  •*-  (12  X  15)  =  39  pounds  per 
square  inch,  which  is  less  than  the  working  value  allowed  in 
concrete. 

The  left  cantilever  or  toe  has  an  upward  pressure.  At  the 
extreme  end  it  is  4,240  pounds  and  at  the  face  of  the  vertical 
wall  it  is  3,200  (scaled  from  Fig.  42).  The  average  pressure 
is  (4,240  +  3,200)  -*-  2  =  3,720  pounds.  The  moment  is, 
therefore, 

M  =  3,720  X  ^  X  12  =  33,480  in.-lb. 
& 

Let  d  =  15,  b  =  12,  and  solve  for  E. 

12  X I52  X  E  =  33,480 
E  =  12.4 

This  value  of  12.4  for  E  is  smaller  than  is  found  in  Fig.  20. 
Since  the  bars  in  the  vertical  slab  are  bent  in  such  a  shape  as  to 
supply  this  tension,  no  further  consideration  of  this  stress  is 
necessary  in  this  problem. 

Some  longitudinal  bars  must  be  placed  in  the  wall  to  pre- 
vent temperature  cracks,  and  also  to. tie  the  concrete  together. 
About  .003  per  cent  of  the  area  above  the  ground  is  often 
used.  In  this  case  f-inch  round  bars  spaced  18  inches  on 
centers  will  be  placed. 


REINFORCED  CONCRETE 


139 


Reinforced  Concrete  Walls  with  Counterforts.  In  this 
type  of  wall  the  vertical  slab  is  supported  by  the  counterforts, 
the  principal  steel  being  horizontal.  The  counterforts  act  as 
cantilever  beams,  being  supported  by  the  footing, 

Illustrative  Example.  Design  a  reinforced  concrete  wall 
with  counterforts,  the  wall  to  be  20  feet  high  and  the  fill  to  be 
level  with  the  top  of  the  wall. 

The  spacing  of  the  counterforts  is  first  determined.  The 
economical  spacing  will  vary  from  8  feet  to  12  feet  or  more, 


Fig.  43.  Design  Diagram  for  Retaining  Wall  with  Counterforts 

depending  on  the  height  of  the  wall.  A  spacing  of  9  feet  on 
centers  will  be  used  for  the  counterforts  in  this  case,  Fig.  43. 
The  maximum  load  on  the  slab  is  on  the  bottom  unit  and  it 
decreases  uniformly  to  zero  at  the  top,  when  the  earth  is 
horizontal  with  the  top  of  the  wall,  as  in  this  case.  Assume 
that  the  base  plate  will  be  18  inches  iu  thickness;  then  the 
center  of  the  bottom  foot  of  slab  will  be  18  feet  from  the  top 
of  the  wall.  The  pressure  to  be  sustained  by  the  lower  foot 
of  the  slab  will  then  be 


140  REINFORCED  CONCRETE 

in  which  P  represents  the  intensity  of  the  horizontal  pressure 
at  any  depth  h,  while  -w  represents  the  weight  per  cubic  foot 
of  the  earth. 

P  =  \  X  100  X  18 
o 

=  600  Ib.  per  sq.  ft. 

Multiplying  this  value  of  P  by  the  distance  between  the  centers 
of  the  counterforts  (600X9  =  5,400)  gives  the  value  of  the 
full  load. 


) 

o 

Placing-  this  value  of  M  equal  to  95  bd2  in  which  b  —  12,  and 
solving  for  d,  we  have 

95  X  12  d2  =  72,900 
d2  =  64 
d  =8  in. 

Adding  2  inches  to  this  for  protecting  the  steel,  the  total 
thickness  of  the  wall  will  be  10  inches.  For  convenience  of 
construction  the  slab  will  be  made  uniform  in  thickness.  The 
steel  for  the  bottom  inch  will  be  .00675  X  18  =  .054  square 
inch.  Round  bars  f  inch  in  diameter  may  be  used  and  spaced 
(.60  -*-  .054  =  11)  11  inches  on  centers.  This  size  of  bars  and 
spacing  should  be  used  for  one-fourth  the  height  of  the  wall. 
The  next  quarter  will  be  reduced  twenty-five  per  cent,  and 
f-inch  round  bars,  spaced  11  inches,  will  be  used.  In  the  third 
quarter,  the  required  area  will  be  one-half  of  that  for  the  first 
quarter.  The  steel  for  this  section  will  be  .054  -*-  2  =  .027 
square  inch,  and  the  bars  will  be  (.44-*-  .027  =  16)  2-inch 
round  bars  spaced  16  inches  on  centers.  In  the  upper  part  of 
the  wall  f-inch  round  bars,  spaced  18  inches  on  centers,  should 
be  used. 

In  order  to  determine  the  requirements  of  the  counterforts 
it  will  be  necessary  to  determine  the  horizontal  pressure  against 


REINFORCED  CONCRETE  141 

a  section  of  the  wall  9  feet  long.     Equation   (21)  has  already 
been  stated  thus: 


Substituting  in  the  modified  form  of  Equation  (21a)  and  mul- 
tiplying by  9,  we  have 

E  =  .286  X  10°  X018'52  X  9  =  44,048  Ib. 

a 

This  load  is  applied  at  one-third  of  the  height  of  the  wall, 
which  is  6.5  feet  above  the  base.  The  moment  in  the  counter- 
fort is 

M  =  44,048  X  6i  X  12  =  3,435,744  in.-lb. 

The  width  of  counterfort  must  be  sufficient  to  insure  rigidity, 
to  resist  any  unequal  pressures,  and  to  imbed  thoroughly  the 
reinforcing  steel.  The  width  is  determined  by  judgment  and 
in  this  case  will  be  made  12  inches  wide.  The  counterfort  and 
vertical  slab  together  form  a  T-beam  with  a  depth  at  the  bot- 
tom of  84  inches.  Let  4  inches  be  allowed  to  the  center  of  the 
steel  ;  then  d  —  80  inches,  jd  =  .87  d  =  .87  X  80  =  69.6  inches. 

M  =  A8X  jd  X  16,000 
3,435,744  =  As  X  69.6  X  16,000 
As  =  3.0  sq.  in. 

Four  1-inch  round  bars  will  give  this  area.  Two  of  these  bars 
will  extend  to  the  top  of  the  wall  and  two  may  be  dropped  off 
at  half  the  height. 

Now  that  these  dimensions  have  been  determined,  the  wall 
will  be  investigated  for  stability  against  overturning.  Substi- 
tuting in  Equation  (21a) 

£  =  .286X  100X20  °  =  5;7201b 
2 

To  find  the  center  of  gravity  of  the  wall,  it  will  be  necessary 
to  take  a  section  9  feet  long,  that  is,  center  to  center  of 
counterforts. 


142 


REINFORCED  CONCRETE 


Center  of  Gravity  of  Concrete 

(Moments  taken  about  a) 


SECTION 

VOLUME 
(Cu.  Ft.) 

MOMENT 
ARM 

VOLUME 
MOMENT 

abed 
e  f  a  h 
hfb 

135.0 
138.8 
57.0 

5.00 
2.92 

5.38 

675.0 
405.3 
306.7 

330.8 

1,387.0 

Distance  from  a  to  center  of  gravity  =  1,387.0  -*-  330.8  = 
4.19  ft. 

Weight  of  9  feet  of  wall  =  330.8  X  3.50  =  49,620  Ib. 

Static  moment  about  a  for  section  9  feet  long  =  49,620  X 
4.19  =  207,908  f  t.-lb. 

Center  of  Gravity  of  Earth 

(Moments  taken  about  a) 


SECTION 

VOLUME 
(Cu.  Ft.) 

MOMENT 
ARM 

VOLUME 
MOMENT 

fblh 
blh 

987.0 
66.4 

6.66 
7.77 

6,573.4 
515.9 

7,089.3 

1,053.4 

Distance  from  a  to  center  of  gravity  =  7,089.3  -*-  1,053.4  = 
6.73  ft. 

Weight  of  earth  per  9  feet  of  wall  =  1,053.4  X  100  = 
105,340  Ib. 

Static  moment  about  a,  for  section  9  feet  long  =  105,340  X 
G.73  =  708,930  ft.-lb. 

Distance  from  a  to  the  resultant  of  the  concrete  and  earth 

207,908  +  708,930  =  916,838  = 
49,620  + 105,340       154,960 

Drawn  the  line  Wc  +  Wr  at  a  distance  5.92  feet  from  a  ami 
produce  the  line  E  to  meet  it.  From  the  intersection  of  these 
two  lines  lay  off  the  sum  of  the  weight  of  the  concrete  plus  the 
weight  of  the  earth,  at  any  convenient  scale.  At  the  end  of  this 
distance  draw  a  line  parallel  to  E  and  lay  off  on  it  the  value 


REINFORCED  CONCRETE  143 

found  for  E.  Draw  the  resultant  R.  This  line  produced  on 
to  the  base  falls  within  the  middle  third,  and  therefore,  the 
wall  should  be  safe  against  overturning. 

Since  the  resultant  cuts  the  base  within  the  middle  third,  Q 
is  greater  than  one-third  of  the  width  of  the  base  and  Equa- 
tions (21d)  and  (21e)  will  be  applied  in  finding  the  pressure 
on  the  base.  Substituting  in  Equation  (21d), 

Pressure  at  the  toe  =  (4 B  —  6  Q)  ~ 

i> 

1  ^4.  Qfifl 

=  [(4  X  10)  -  (6  X  3.73)]     ^ 
=  27,304  Ib. 

Dividing  27,304  by  9  we  have  3,034  pounds,  which  is  the  weight 
per  foot  in  length  of  the  wall  on  the  toe. 

The  pressure  at  the  heel  is  found  by  substituting  in  Equa- 
tion (21e) 

p 

Pressure  at  the  heel  =  (6  $  —  2  #)  ^ 

S3 

=  [(6  X  3.73)  -  (2  X  10)]154!£60 
=  3,688  Ib. 

Dividing  3,688  by  9  gives  410  pounds,  which  is  the  weight,  per 
lineal  foot  at  the  heel. 

In  designing  the  toe  (left  cantilever)  there  is  the  average 
pressure,  (3,034  +  2,378)^2  =  2,706,  for  which  steel  must 
be  provided. 

2,706  X  2.5  =  6,765 

M  =  6,765  X  M  x  12  =  101,475  in.-lb. 

<L 

If  6  =  12  and  d  =  l5  (the  total  thickness  allowed  was  18 
inches),  solving  for  E,  we  have 

12  X  15-  X  R  =  101,475 
72  =  38 


144  REINFORCED  CONCRETE 

Therefore  c  equals  300  and  s  equals  12,000  approximately, 
and  p  equals  .0035.  The  steel  per  lineal  foot  of  wall  required 
will  be  12  X  15  X  .0035  =  .63  square  inches,  and  this  is  equal 
to  f-inch  round  bars  spaced  11  inches  on  centers.  As  a  pre- 
caution against  the  load  being  concentrated  under  the  counter- 
forts, three  extra  bars  should  be  placed  in  the  toe  at  these 
places. 

The  rear  portion  of  the  footing-  is  designed  as  a  simple  beam 
between  the  counterforts.  It  must  have  sufficient  strength  to 
support  the  earth  above  it  and  also  its  own  weight,  although. 
as  explained  previously  for  the  L-shaped  wall,  such  a  stress 
cannot  be  developed  unless  the  wall  were  just  at  the  point  of 
overturning,  and  the  investigation  for  stability  shows  that  this 
cannot  happen.  The  following  calculation,  therefore,  intro- 
duces in  the  design  of  the  base  slab  an  additional  factor  of 
safety,  of  perhaps  2,  besides  the  usual  working  factor  of 
about  4. 

Weight  of  earth  =  105,340  Ib. 

Weight  of  base  =   13.500  Ib. 

118,840  Ib. 

118,840  X  0  X  12 

M  =  —  =  1,604,340  in.-lb. 

8 

If  &  =  80  and  d  =  15,  solving  for  E,  we  have 

80  X  15"2  X  E  =  1,604,340 
£  =  89 

From  Fig.  20  we  find  that  with  steel  stressed  to  16,000 
pounds  the  concrete  would  be  stressed  to  about  575.  pounds  per 
square  inch  and  the  required  percentage  of  steel  would  be 
.0062.  The  bars  required  will  be  (.0062  X  80  X  15  =  7.44  square 
inches)  nine  bars  1  inch  round  spaced  8  inches  apart. 

In  addition  to  the  steel  that  has  been  required  to  satisfy  the 
different  equations,  the  bars  in  the  vertical  slab  and  those  in 
the  rear  portion  of  the  footing  must  be  tied  to  the  counter- 
forts. (See  Fig.  43.)  A  few  bars  should  also  be  placed  in 
the  top  of  the  footing,  but  no  definite  calculation  can  be  made 


REINFORCED  CONCRETE 


145 


for  them.  The  vertical  slab  should  be  reinforced  for  tempera- 
ture stresses.  In  this  wall  I-inch  round  bars  spaced  18  inches 
on  centers  will  be  used. 

Coping  and  Anchorages.  Retaining  walls  generally  have 
a  coping  at  the  top.  This  can  be  made  to  suit  the  conditions 
or  to  accord  with  the  wish  of  the  designer.  When  reinforced 
concrete  walls  are  not  stable  against-  sliding,  they  can  be 
anchored  by  making  a  projection  of  the  bottom  into  the 
foundation.  This  is  shown  in  Figs.  42  and  43. 

CULVERTS 

A  flat  slab  design  is  generally  used  for  spans  up  to  20  feet, 
for  both  highway  and  railroad  culverts.  In  highway  construc- 
tion, it  is  sometimes  found  more  economical  to  use  the  girder 
bridge  for  spans  as  short  as  14  or  16  feet.  The  present  dis- 
cussion will  be  confined  to  box  culverts  for  highway  use.  Con- 
crete, ni:d  particularly  reinforced  concrete,  is  now  much  used 


K-  30-0  FOR  60  TON  CRR — -| 


Fig.  44.     Load  Diagram  for  60-Ton  and  40-Ton  Electric  Cars 

for  culverts  and  bridges.  Its  permanence  and  freedom  from 
maintenance  charges,  compared  with  wood  and  with  steel 
structures,  are  much  in  its  favor. 

Classification  by  Loadings.  Highway  structures  are  usually 
divided  into  three  classes,  as  follows: 

Class  No.  1.  Light  structures  for  ordinary  country  use 
where  the  heaviest  load  may  be  taken  as  a  12-ton  road  roller; 
the  uniform  live  load,  100  pounds  per  square  foot. 

Class  No.  2.  Heavy  structures  for  use  where  20-ton  road 
rollers  and  electric  cars  of  a  minimum  weight  of  40  tons  must 


146 


REINFORCED  CONCRETE 


be  provided  for;  the  uniform  distributed  load,  125  pounds  per 
square  foot. 

Class  No.  3.  City  structures  for  heavy  concentrated  loads, 
such  as  large  interurban  cars,  weighing-  60  tons;  the  uniform 
distributed  load,  350  pounds  per  square  foot. 

Load  Diagrams.  Diagrams  representing  the  loadings  for 
40-  and  60-ton  cars,  and  for  road  rollers  are  shown  in  Figs. 
44  and  45  respectively.  Since  short-span  structures  are  being- 
considered,  only  one  truck  of  a  car  will  be  on  the  culvert  at  one 

time.  The  truck  of  a  car 
will  be  considered  as  dis- 
tributing the  load  over 
an  area  which  is  two  feet 
longer  than  the  center  to 
center  of  the  wheels,  and 
has  a  width  equal  to  the 
length  of  the  ties,  usual- 
ly 8  feet.  The  fill  will 
further  distribute  this 
load  on  a  slope  of  |  to  1. 
The  fill  over  a  culvert 
should  never  be  less  than 
one  foot.  For  fast- 
moving  cars  the  bending 
moment  for  the  live  load 
should  be  increased  35 
per  cent  for  impact  for 
Fig.  45.  Load  Diagram  for  Road  Roller  fills  of  less  than  five  f  eet- 

Example.  Design  a  flat-slab  culvert  with  a  span  of  15  feet  to  support 
a  fill  of  4  feet  under  the  ties,  a  macadam  roadway,  and  a  40-ton  car. 

Solution.  The  top  will  be  considered  first  and  a  width  of  one  foot 
will  be  taken.  The  fill  at  100  pounds  per  cubic  foot  will  equal  100  X  4 
X  15  =  6,000  pounds.  The  macadam  will  have  a  thickness  of  the  rail 
plus  the  tie,  which  will  be  about  12  inches.  This  material  at  125 
pounds  per  cubic  foot  will  equal  125  X  1  X  15  =  1,875  pounds  for  a 
strip  one  foot  wide.  The  maximum  bending  moment  for  the  live  load 
will  occur  when  one  of  the  trucks  of  a  car  is  at  the  middle  of  the  span. 
The  load,  20  tons,  will  be  distributed  over  an  area,  as  shown  in  Fig.  40, 
9  feet  by  10  feet  =  90  square  feet.  A  strip  one  foot  wide  then  must 
support  20  X  2,000  -f- 10  =  4,000  pounds. 


REINFORCED  CONCRETE  147 

The  formula  for  this  bending  moment  would  be 


Substituting  in  this  formula,  we  have 

M  =    (4,000  >  X  IB  _  4,000X9  V 

\  4  o          ' 

30  per  cent  added  for  impact         =    37,800  in.-lb. 

Total  moment  for  live  load  =  163,800  in.-lb. 

Assume  that  the  slab  will  be  22  inches  thick  ;  then  a  strip  one  foot 
wide  weighs  1|  X  15  X  150  —  4,125  pounds.  The  total  weight  of  the 
811,  macadam  and  concrete,  is  12,000  pounds.  The  moment  for  this 
load  is 

12.000X15X12 


Moment  for  live  load  =  163,800  in.-lb. 
Total  moment  =  433,800  in.-lb. 

Placing  this  moment  equal  to  95  6  d2,  where  6  =  12,  we  have 

95  X  12  X  (1-  =  433,800 
<P  =  3SO  . 
d  =19.  5  in. 

If  2J  inches  is  added  for  protecting  the  steel,  then  the  total  thickness 
will  be  22  inches.  The  steel  required  equals  .00675  X  12  X  19.5  =  1.5S 
square  inches.  Round  bars  1  inch  in  diameter,  spaced  6  inches  on 
centers,  will  satisfy  this  requirement. 

The  shear  at  the  point  of  supports  will  equal  one-half  the  sum  of  the 
live  and  dead  loads  divided  by  area  of  the  section,  that  is,  (4,000  + 
12,000)  -H  2  =  8,000. 

v  =  8,000  -f-  &./  d 
•=  8,000  -*-  (12  X  .87  X  19.5) 
=  39  lb.  per  sq.  in. 

which  is  much  less  than  the  permissible  working  load.  Even  in  this 
case  one-third  of  the  bars  should  be  turned  up  at  about  3  feet  from  the 
end  of  the  span. 

The  horizontal  pressure  on  the  side  walls  of  the  culvert  produced  by 
the  earth  will  vary  with  the  depth  below  the  surface.  The  center  of  the 
top  foot  of  the  side  walls  is  7.5  feet  and  the  center  of  the  bottom  foot 
is  12.5  feet  below  the  surface  of  the  roadway.  At  the  top,  therefore, 


P_ 


W/I       100  X  7.5 


=  250  lb.  per  sq.  ft. 


At  the  bottom  it  would  be 

100  X  12.5 


The  average  pressure  equals  (250  +  416)  -=-  2  =  333  pounds.  This  is 
not  strictly  accurate  but  sufficiently  so  for  the  side  walls.  The  live 
load  is  4,000  -j-  9  =  444  per  square  foot.  It  will  be  assumed  that  the 
horizontal  pressure  from  the  live  load  equals  444  -=-  3  =  148  pounds  per 


148 


REINFORCED  CONCRETE 


square  foot,  this  load  being  independent  of  the  depth  of  the  fill.  The 
total  livo  and  dead 'load  is  therefore,  533  +  148  =  481  pounds  per  square 
foot.  The  bending  moment  for  this  load  is 


JMt.    Q  /N     J-—    -  ,,  /^     J.^- 

O  O 

A  slab  with  a  thickness  of  7  inches  would  satisfy  this  equation.  Since 
the  side  walls  must  support  the  top  slab  as  well  as  the  side  pressures, 
they  should  not  bo  much  less  in  thickness  than  the  top.  Make  the  walls 
15  inches  thick  and  reinforce  them  as  shown  in  Fig.  46. 

The  bottom  is  sometimes  made  the  same  as  the  top.    This  is 
not  necessary  unless  the  foundation  is  very  soft  and  the  load 


/. 


—, — 15'° 
i'*(,"c.-c 


:\ 


Fig.  46.    Design  Diagram  for  Flat-Slab  Cul- 
vert with  15-Foot  Span 

must  be  distributed  over  the  whole  area.  In  this  ease  it  will 
be  made  the  same  as  the  side  walls  and  reinforced  as  shown. 
In  designing  the  culvert,  the  student  will  note  that  while 
some  of  the  calculations  are  definite  other  dimensions  must  be 
assumed.  The  fillets  in  the  corners  will  assist  in  stiffening  the 
structure.  Wing  walls  must  be  provided  at  the  ends.  Longi- 
tudinal reinforcement  also  must  be  provided. 

Example.  Design  a  box  culvert  5  feet  square  to  support  a  road  roller 
weighing  12  tons  (Class  No.  1),  fill  2  feet  deep. 

Solution.  The  maximum  load  will  occur  when  the  rear  wheel  is  at 
the  center  of  the  span,  which  is  two-thirds  of  12  tons,  or  8  tons,  Fig.  47. 
This  will  be  distributed  over  an  area  of  1  foot  by  9  feet  6  inches.  The 
live  load  is  therefore  8  X  2,000  +  9.5  =  1,664  pounds  for  a  strip  one  foot 


REINFORCED  CONCRETE 


149 


wide.  The  dead  load  will  be  100  X  2  =  200  pounds  per  square  foot  for 
fill  and,  assuming  that  the  top  slab  will  be  8  inches  thick,  12.5  X  8  =  100 
pounds  per  square  foot.  The  moments  will  be  as  follows : 


Live  load  M  =  --  X  12  = 


V  *» 

* 


X  12       =  24,960  in.-lb. 


35  per  cent  added  for  impact  =  24,960  X  .35  =    3,736  in.-lb 

W  I2  300  V  r»2 

Dead  load  M  =  ^-  X  12  =         *        X  12      -=  11,250  iu.-lb 

Total  Moment  =  44,946  in.-lb 


Placing  this  equal  to  95  6  d2  where  6  =  12, 

95  X  12  Xd2  =  44,946 
d*  =  39.43 
d  =    6.28  in. 

Make  the  total  thickness  8  inches.  The  steel  required  will  be  .00675  X 
C.28  =  .04239  square  inch  per  inch  of  width,  and  |-inch  round  bars 
spaced  10  inchos  on  centers  will  fulfil  the 
requirements. 

The  earth  pressure  on  the  sides  is  as 
follows :  /      8  TONS 


At  the  top 


At  the  bottom 


Wh       100  X  3.2 

3     =  3 

106  Ib.  per  sq.  ft. 

Wh       100  X  7.2 


240  Ib.  per  sq.  ft. 


Average  pressure       (.106  +  240)  +  2 
=?=  173  Ib.  per  sq.  ft. 

Pressure  for  live  load      1,664  -*-  3 

=  555  Ib.  per  sq.  ft. 


Total  pressure 


173'+  555 
=  728.  Ib. 


The  bending  moment  for  this  load  is 
M  =«£x  12  = 


27.300  in.-lb. 


Fig.  47.  Design  Diagram  for 
Box  Culvert  5  Feet  Square 


A  slab  7  inches  thick  will  more  than  satisfy  this  equation;  but  to 
insure  stiffness  the  sides  for  a  culvert  of  this  size  should  not  be  made 
less  than  the  thickness  of  the  top.  Use  |-inch  round  bars,  spaced  9 
inches  on  centers,  Fig.  47.  The  bottom  will  be  made  8  inches  thick, 
also,  and  reinforced  with  1-inch  round  bars,  spaced  10  inches  on  centers. 
Temperature  bars  must  also  be  provided. 


150 


REINFORCED  CONCRETE 


GIRDER  BRIDGES 

Method  of  Design.  Giider  bridges  are  being  extensively 
used  for  country  highways  for  spans  from  20  to  40  feet.  They 
are  sometimes  used  for  spans  up  to  GO  feet  and  often  for  spans 
as  short  as  16  feet.  Fig.  48  shows  the  section  of  one-half  the 
width  of  such  a  bridge.  The  slab  for  a  bridge  of  this  kind 
must  always  be  paved  or  macadamized  so  that  no  wheels  will 
come  directly  on  the  concrete. 

Illustrative  Example.  Design  a  girder  bridge  with  a  clear 
span  of  26  feet ;  the  width  of  roadway  is  16  feet  and  there  are 


Fig.  48.    Design  Diagram  for  Girder  Bridge 

two  sidewalks,  each  4  feet  6  inches  wide.  The  loading  for  this 
bridge  is  to  be  as  specified  for  Class  No.  2,  given  on  page  145, 
the  car  line  to  be  in  the  center  of  the  bridge,  and  a  fill  of  six 
inches  to  be  placed  under  the  ties  with  a  macadam-surfaced 
roadway. 

The  slab  for  such  a  structure  should  never  be  less,  than  5 
inches  thick  on  account  of  concentrated  loads  and  shear  due  to 
road  rollers  and  other  such  loads.  To  cover  such  contingencies 
the  slab  will  be  designed  for  a  live  load  of  500  pounds  per 
square  foot.  The  slab  load  and  moment,  therefore,  will  be 
as  follows: 


REINFORCED  CONCRETE  151 

Live  load  4  X  1  X  500  =  2,000  Ib. 

Slab,  5  in.  rs  X  150  X  4  =     250  Ib. 

Fill,  20  in.  Ij}  X  125  X  4  =     833  Ib. 

Total  load  =  3,083  Ib. 


o 


=  n_.l 


Placing  this  moment  equal  to  95  bd2,  where  b  =  12,  and 
solving,  we  find  that  d  =  4  inches. 

The  steel  area  must,  therefore,  equal  .00675  X  4  X  12  =  .32 
square  inches  per  foot  of  width,  which  requires  f-inch  round 
bars,  spaced  4  inches  on  centers. 

The  outside  girder  (£a),  Fig.  48,  supports  one-half  of  the 
sidewalk  'load,  which  is  as  follows: 

Live  load  125  125  X  2;}  X  26           =    7,313  Ib. 

Walk  4  in.  thick  50  X  2]  X  26              =    2,925.1b. 

Cinder  fill  15  in.  60  X  1£  X  2|  X  26  =    4,388  Ib. 

Slab  5  in.  60  X  2|  X  26              =    3,510  Ib. 

Girder  12  X  54  in.  150  X  4J  X  26  X  1    =  17,550  Ib. 

Total  load  =  35,686  Ib. 

35,686  X  26  X  12 
M  =  -  =  1,391,754  in.-lb. 

o 

This  moment  placed  equal  to  95  bd2,  when  b  =  12,  would 
irequire  a  depth  of  35  inches  to  the  center  of  the  steel,  while  the 
;total  depth  of  the  beam  is  54  inches.  Therefore,  make  b  equal 
12  and  d  equal  51,  and  solve  for  the  moment  factor  R. 

12  X  512  x  R  =  1,391,754 


By  referring  to  the  diagram,  Fig.  20,  it  is  at  once  to  be  seen 
hat  when  R  equals  45  the  compression  in  the  concrete  will  be 
LOW  and  that  a  percentage  of  steel  of  .005  is  more  than  actually 
will  be  required.  However,  .that  amount  will  be  used.  12  X 
51  X  .005  —  3.1  square  inches.  Four  1-inch  round  bars  will 


152 


REINFORCED  CONCRETE 


be  used,  two  bars  to  be  straight  and  two  turned  up  near  the 
ends.  The  shear  per  square  inch  is  small,  but  stirrups  should 
be  used. 

Girder  G.^  will  next  be  designed.     For  this  beam  there  are 
three  live  loads  to  be  considered  and  the  girder  will  be  designed 


(b) 

Fig.  49.   Diagrams  for  Loadings  for  Road  Roller  and  Electric  Car 

to  support  the  maximum  one  combined  with  the  dead  load. 
The  three  live  loads  are:   the  uniform  load  of  125  pounds  per 
square  foot,  a  20-ton  road  roller,  and  a  40-ton  electric  car. 
The  dead  load  and  moment  for  this  load  will  be  as  follows : 


REINFORCED  CONCRETE  153 

Macadam  and  fill  l-§  X  125  X  5  X  26  =  27,084  Ib. 

Slab  A  X  150  X  5  X  26  =    8,125'  Ib. 

Beam  12"  X  24"  1  X  2  X  150  X  26  =    7,800  Ib. 

(assumed) 

Total  load  =  43,009  Ib. 

43,009  X  26  X  12 
M  =  —  -  -  Q  -  =  1,677,351  m.-lb. 

o 

The  total  live  load  for  a  uniform  loading  of  125  pounds 
per  square  foot  would  be  125  X  5  X  26  =  16,250  pounds,  and 
its  moment  would  be 

1M50X26X12 


O 

Since  the  fill  is  so  small  the  weight  of  a  road  roller  or  -car 
cannot  be  distributed  to  any  great  amount  by  this  means,  it  will 
not  be  considered  in  the  calculations.  Each  of  these  beams 
may  be  required  to  support  the  whole  weight  of  the  front  wheel 
and  half  the  weight  of  the  rear  wheel.  This  moment  will  be  a 
maximum  when  one  wheel  is  one-fourth  of  the  distance 
between  the  center  of  wheels  from  the  center  of  the  span  of 
the  bridge. 

The  maximum  reaction  is  at  the  right  and  is 

_  13,333  X  4.75  ,  13,333  X  15.75  _ 
E~        -~~ 


26  ' 

Then 

M  =  10,478  X  10.25  X  12  =  1,288,794  m.-lb. 
The  maximum  load  produced  on  girders  G3  by  an  electric 
car  takes  place  when  one  of  the  trucks  is  at  the  center  of  the 
span.  Each  of  these  girders  at  that  time  would  be  supporting 
one-fourth  of  the  total  weight  of  40  tons,  or  10  tons.  (See 
Fig.  49.)  The  moment  is,  therefore, 

26       20.000  X  7 


35  per  cent  added  for  impact  =     472,500  in.-lb. 

Total  =  1,822,500  in.-lb. 

The  electric  car  produces  a  greater  bending  moment  than 


154  REINFORCED  CONCRETE 

either  of  the  other  live  loads  and,  therefore,  will  be  used 
together  with  the  dead  load.  That  is,  1,822,500  +  1,677,351  = 
3,499,851.  Let  d  equal  25.5 ;  then  25.5  X  .88  =  22.4  inches. 
The  required  amount  of  steel  then  is  3,499,851  •*•  (22.4  X 
16,000)  =9.8  square  inches.  Eight  bars  1|  inches  in  diameter 
will  be  used,  one-half  of  which  will  be  turned  up  in  pairs  at 
different  points  near  the  ends  of  the  girder. 

The  shear  in  this  girder  will  be  one-half  the  sum  of  20,000 
and  43,000,  or  31,500  pounds.  Then 

31,500 

v  =  p-,  x  22  =  H4  Ib.  per  sq.  in. 

Therefore  stirrups  must  be  used.  They  should  be  f  of  an  inch 
in  diameter,  used  throughout  the  length  of  the  girder,  and 
spaced  not  over  6  inches  apart  near  the  ends  of  the  girders. 

The  bending  moment  for  girder  G2  will  be  taken  as  the  mean 
of  girders  G±  and  G3,  plus  the  dead  load,  and  will  be  as  follows : 

£1  =  1,505,400  in.-lb. 
G*  =  3,499,500  in.-lb. 
5,004,900  in.-lb. 
.'•  G2  =  5,004,900  -*-  2  =  2,502,450  in.-lb. 

The  steel  required  equals  2,502,450  +  (22.4  X  16,000)  =  7 
square  inches.  Seven  bars  1J  inches  in  diameter  will  be  used, 
three-eighths  of  which  will  be  turned  up  near  the  ends  of  the 
girders.  Use  |-inch  shear  bars. 

In  designing  girder  bridges  the  designer  must  always  investi- 
gate the  shear  in  the  girders  and  the  compression  in  the  T-beams 
very  carefully  and  see  that  these  stresses  are  satisfied. 

CONCRETE  BUILDING  BLOCKS 

Concrete  blocks  are  sometimes  used  for  the  walls  of  houses, 
bams,  and  factory  buildings  of  one  to  four  stories.  They  are 
made  at  a  factory  or  on  the  site  of  the  work,  and  are  placed  in 
the  wall  in  the  same  manner  as  brick  or  stone.  The  blocks  are 
made  in  metal  machines,  being  molded  somewhat  similarly  to 
brick. 


REINFORCED  CONCRETE  155 

.  Types.  There  are  two  general  types  of  blocks — solid  blocks 
and  hollow  blocks.  The  solid  blocks  are  used  for  heavy  work 
and  vary  in  size  according  to  different  classes  of  work.  The 
hollow  blocks  are  used  for  the  walls  of  buildings,  and  this  is 
the  type  generally  referred  to  when  concrete  building  blocks 
are  mentioned.  They  are  cheaper  than  the  solid  blocks  and  are 
less  easily  penetrated  by  water,  cold,  and  heat.  There  are  also 
two  types  of  the  hollow  blocks— the  one-piece  block  and  the 
two-piece  block.  The  one-piece  type  consists  of  a  block,  with 
hollow  cores,  making  the  whole  thickness  of  the  wall.  In  the 
two-piece  type,  the  front  and  back  of  the  blocks  are  made  in 
separate  pieces  and  bonded  when  laid  up  in  the  wall :  this  bond 
is  secured  either  by  the  blocks  lapping  over  each  other  or  by  the 
use  of  galvanized  iron  ties.  Hollow  blocks  are  also  made  with 
two  cores.  Fig.  50  shows  the  different  types  of  hollow  blocks. 


Fig.  50.     Types  of  Hollow  Concrete  Blocks 

There  are  a  great  variety  of  machines  in  use  for  the  manu- 
facture of  concrete  hollow  blocks.  Some  types  of  these  machines 
will  be  discussed  in  the  section  devoted  to  machinery. 

Sizes.  Various  shapes  and  sizes  of  blocks  are  made. 
Builders  of  some  of  the  standard  machines  have  adopted  a 
length  of  32  inches  and  a  height  of  9  inches  for  the  full-sized 
blocks,  with  widths  of  8,  10,  and  12  inches.  Lengths  of  8,  12, 
16,  20,  and  24  inches  are  made  with  the  same  machine,  by  the 
use  of  parting-plates  and  suitably  divided  face-plates.  Most 
machines  are  constructed  so  that  any  length  between  4  and  32 
inches,  and  any  desired  height,  can  be  obtained. 

The  size  of  the  openings  (the  cores)  varies  from  one-third 
to  one-half  of  the  surface  of  the  top  or  bottom  of  the  block. 
The  building  laws  of  many  cities  state  that  the  openings  shall 
amount  to  only  one-third  of  the  surface.  For  any  ordinary 


156  REINFORCED  CONCRETE 

purpose,  blocks  with  50  per  cent  open  space  are  stronger  than 
necessary. 

Materials.  The  materials  for  making  concrete  blocks  con- 
sist of  Portland  cement,  sand,  and  crushed  stone  or  gravel. 
Because  of  the  narrow  space  to  be  filled  with  concrete,  the 
stone  and  gravel  are  limited  to  |  or  f  inch;  at  least  one-third 
of  the  material,  by  weight,  should  be  coarser  than  |  inch. 

The  proportions  of  the  materials  must  be  such  that  a  dense 
'and  water-tight  concrete  is  secured.  Cement  and  a  fine  sand 
of  uniform  size,  made  into  a  mortar  and  used  without  the  addi- 
tion of  any  coarse  material,  will  not  produce  good  results.  A 
mixture  of  1  pprt  Portland  cement  and  4  or  6  parts  of  a  coarse 
sand  ranging  in  size  from  dust  to  J  inch  will  make  good  blocks 
when  mixed  wet  and  well  tamped.  The  proportions  should 
rever  be  leaner  than  1:2:4  if  good  blocks  are  required. 

Architectural  features  often  require  a  special  facing  for 
blocks.  This  can  be  secured  by  mixing  marble  dust  with  white 
Portland  cement  for  a  white  block,  or  granite  chips  with  Port- 
land cement  for  a  granite  finish.  The  facing-material  is  made 
into  a  mortar  and  placed  against  that  side  of  the  form  which 
is  to  make  the  face  of  the  block.  This  face  may  be  either  a 
plain  face  or  of  various  ornamental  patterns,  as  tool-faced, 
paneled,  broken  ashlar,  etc.  The  penetration  of  water  may  be 
effectively  prevented  by  this  rich  coat. 

Blocks  made  with  di^  concrete  will  be  weak  and  porous  even 
if  they  are  well  sprinkled  after  being  removed  from  the  forms. 
If  the  concrete  is  made  too  wet  it  will  stick  to  the  sides  of  the 
plates,  and  the  blocks  will  settle  out  of  shape  if  they  are 
removed  promptly  from  the  mold.  There  should  be,  therefore, 
as  much  water  as  can  be  used  without  causing  the  block  to  stick 
or  sag  out  of  shf.pe  when  removed  from  the  molds.  The  amount 
of  water  is  usually  from  8  to  12  per  cent  of  the  weight  of  the 
dry  mixture.  To  secure  blocks  uniform  in  strength  and  color, 
the  same  amount  of  wate'r  must  be  used  for  every  batch. 

Mixing  and  Tamping.  Concrete  for  blocks  must  be  well 
mixed.  This  can  best  be  done  in  a  batch  mixer,  although  good 
results  can  be  attained  by  hand  mixing.  Power  pressure  applied 


REINFORCED  CONCRETE  157 

to  the  concrete  is  better  than  hand  tamping,  because  it  is  more 
evenly  distributed  over  the  whole  area  of  the  block. 

Curing  of  Blocks.  Air  Curing.  The  blocks  are  removed 
from  the  machine  on  a  steel  plate,  on  which  they  should  remain 
for  24  hours.  The  blocks  should  be  protected  from  the  sun  and 
dry  winds  for  at  least  a  week,  and  thoroughly  sprinkled  fre- 
quently. They  should  be  at  least  four  weeks  old  before  they  are 
placed  in  a  wall ;  if  they  are  built  up  in  a  wall  while  green, 
shrinkage  cracks  will  be  likely  to  occur  in  the  joints. 

Steam  Curing.  Concrete  blocks  can  be  cured  much  more 
quickly  in  a  steam  chamber  than  in  the  open  air.  They  should  be 
left  in  the  steam  chamber  for  48  hours  at  a  pressure  of  80 
pounds  per  square  inch.  By  this  method,  blocks  can  be  handled 
and  used  much  more  quickly  than  when  air  cured,  and  their 
strength  is  much  higher  than  the  air-cured  blocks  when  six 
months  old.  When  a  large  quantity  of  blocks  is  to  be  made,  the 
steam  curing  is  more  economical  than  the  air  curing,  even  con- 
sidering the  much  more  expensive  plant  that  is  required.* 

Cost  of  Making.  The  following  example  of  the  cost  of 
making  concrete  blocks  is  quoted  from  a  paper  by  Mr.  N.  F. 
Palmer,  C.  E. : 

Blocks  8  by  9  by  32  inches ;  gang  consisted  of  five  workmen  and  a 
foreman  ;  record  for  one  hour,  30  blocks  ;  general  average  for  10  hours, 
200  blocks.  The  itemized  cost  was  as  follows  : 

1  foreman  @   $2.50 $  2.50 

5  helpers  @     2.00 10.00 

13  bbls.  cement  @      2.00 26.00 

10  cu.  yds.  sand  and  gravel  @     1.00 10.00 

Interest  and  depreciation  on  machine 2.00 

Total     $50.50 

This  is  the  equivalent  of  $50.50  -=-  200,  or  25|  cents  per  block  ;  or? 
since  the  face  of  the  block  was  9  by  32  inches,  or  exactly  2  square  feet, 
the  equivalent  of  12.6  cents  per  square  foot  of  an  8-inch  wall. 

Another  illustration,  quoted  from  GUlette,  for  a  10-inch  wall, 
was  itemized  as  follows,  for  each  square  foot  of  wall: 

Sand     $  0.020 

Cement  @  $1.60  per  barrel .045 

Labor  @  $1.83  per  day 038 

Total  per  square  foot $  0.103 

*  See  Technological  Papers  Bureau  of  Standards  (U.  S.),  No.  5. 


158 


REINFORCED  CONCRETE 


This  is  apparently  considerably  cheaper  than  the  first  case,  even  after 
allowing  for  the  fact  that  the  second  case  does  not  provide  for  interest, 
depreciation  on  plant,  etc.,  which  in  the  first  case  is  only  4  per  cent 
of  the  total.  The  allowance  of  4  per  cent  is  probably  too  small. 

Cement  Brick.  Cement  brick  are  made  of  the  same  pro- 
portions of  material  as  concrete  blocks.  In  general,  what  has 
been  said  about  concrete  blocks  applies  also  to  cement  brick. 
They  have  not  been  extensively  used. 

FENCE  POSTS 

Design.  Reinforced  concrete  fence  posts  are  now  being 
extensively  used.  They  have  many  of  the  advantages  of  wooden 
posts  and  few  of  the  disadvantages.  In  first  cost,  concrete 


Fig.  51.     Cross  Section  of  Triangular  Fence  Post 

posts  may  be  more  or  less  expensive  than  the  wooden  posts, 
depending  on  the  local  supply  of  timber  suitable  for  posts  and 
the  local  supply  of  materials  for  making  concrete. 

Concrete  posts  are  made  in  several  shapes  and  sizes.  Posts 
square  in  cross  section  and  having  the  same  section  throughout 
their  length  are  perhaps  the  simplest  to  make,  but  posts  taper- 
ing from  the  bottom  to  the  top  on  two  sides  or  on  all  four  sides 
will  be  more  economical  in  material,  lighter  to  handle,  and  will 


REINFORCED  CONCRETE 


159 


look  much  better.  For  posts  7  feet  long  the  sections  should  be 
5  inches  square  at  the  bottom  and  taper  to  3^  or  4  inches  square 
at  the  top.  A  i-inch  bar  should  be  placed  in  each  corner  of  the 
post  and  these  bars  should  be  tied  together  by  heavy  wire  loops 
spaced  12  inches  on  centers.  Corner  and  gate  posts  must  be 
made  larger.  In  Fig.  51  is  shown  a  triangular  section  illustrated 


Fig.  52.     Methods  of  Fastening  Wire  Fencing  to  Concrete  Posts 
in  Farmers'  Bulletin  403,  of  the  U.  S.  Department  of  Agri- 
culture ;  the  section  is  for  a  post  7  feet  long  and  does  not  taper. 
These  posts  must  be  set  so  that  the  narrow  side  will  support  the 
fencing. 

Fastenings.  There  are  several  methods  of  fastening  the 
wire  or  other  fencing  to  the  posts.  Galvanized  staples  or  loops 
may  be  placed  in  the  green  concrete,  or  small  holes  may  be  left 
in  the  center  of  the  posts.  In  Fig.  52  are  shown  two  simple 


160  REINFORCED  CONCRETE 

methods  of  fastening  wire  fencing  given  in  the  Bulletin  already 
mentioned. 

Materials  and  tForms.  The  concrete  should  be  a  1:2:4 
mix  in  which  the  stone  or  gravel  should  not  be  larger  than  \ 
inch.  It  must  be  a  wet  mix,  well  tamped,  and  the  post  fully 
seasoned  before  being  placed.  The  forms  should  be  so  well 
made  that  they  can  be  used  many  times,  and  they  ought  to  be 
carefully  cleaned  and  oiled  each  time. 

SILOS 

Types.  There  are  two  general  ways  in  which  silos  arc 
constructed  of  concrete :  They  may  be  constructed  as  a  mono- 
lith—that is,  the  concrete  poured  into  the  forms— or  with  blocks. 
The  monolithic  walls  may  be  either  one  solid  wall  or  a  double 
wall  with  an  air  space  between  them.  The  blocks  may  also  be 
either  solid  or  hollow.  In  cold  climates  it  is  much  better  to 
have  the  double  or  hollow  walls  to  retard  the  freezing  of  the 
silage. 

Design.  In  the  walls  of  a  silo  there  is  an  outward  pressure 
that  must  be  resisted  by  steel  in  tension.  The  amount  of  this 
pressure  is  not  so  well  known  as  in  the  case  of  water  pressure 
in  a  tank.  Some  state  experiment  stations  have  estimated  the 
silo  pressure  at  11  pounds  per  square  foot,  but  to  be  on  the  safe 
side  it  should  be  taken  as  15  to  20  pounds.  There  is  no  definite 
calculation  that  can  be  made  to  determine  the  thickness  of  the 
concrete  walls.  For  a  solid  concrete  wall  the  thickness  ought 
never  to  be  less  than  6  inches,  and  for  a  large  silo  it  should  be 
at  least  10  inches.  When  double  walls  are  used,  the  inner  one 
should  be  5  inches  thick  and  the  outer  wall  3  or  4  inches  thick, 
with  an  air  space  of  4  inches  between.  The  two  walls  are  con- 
nected every  four  feet,  making  one  solid  wall. 

Blocks  for  silo  walls  should  be  8  or  10  inches  in  thickness. 
There  should  be  a  groove  made  in  the  top  of  the  block  for  the 
reinforcing  steel  to  set  in.  In  this  type  of  construction  there 
is  not  enough  cement  mortar  used  in  the  joints  to  develop  the 
strength  of  the  steel  reinforcement,  and,  therefore,  the  ends 
of  the  bars  should  be  fastened  together  by  clips  or  some  other 


REINFORCED  CONCRETE 


161 


special  device.  The  inside  of  the  wall 
should  be  made  perfectly  smooth  so 
that  the  silage  can  slide  down  with  as 
little  resistance  from  the  wall  as  pos- 
sible. The  roofs  can  be  made  of  rein- 
forced concrete,  tut  a  wooden-  roof  is 
much  cheaper. 

Example.  Design  a  silo  16  feet  In  diam- 
eter and  32  feet  high,  u&ing  solid  concrete 
walls. 

Solution,  For  a  silo  of  these  dimensions 
the  wall  will  be  made  8  inches'  thick.  The 
bursting  pressure  on  the  bottom  foot  of  Che 
wall  will  be  one-half  of  the  height  multi- 
plied by  diameter  •multiplied  by  the  pressure, 
which  Is  (31.5  X 16  X  20)  •-*  2  =  5,040.  The 
amount  of  steel  required  for  the  4ower  foot 
of  the  wall  will  be  5,040 -f- 16,000  =  .32- 
square  inch,  which  is  equivalent  to  J-inc'h 
round  bars  spaced  1\  inches  on  centers. 
These  bars  should  be  used  for  a  height  of  5 
feet.  For  the  next  section  of  5  feet  the 
steel  required  would  be  (26.5  X  16  X' 20) 
-j-  2  =  4,240  -i- 16,000  =  .26  square  inch,  or 
round  bars  spaced  7$  inches  on  centers. 
This  calculation  is  repeated,  as  shown  in 
Fig.  53,  but  the  steel  area  should  never  be 
less  than  |-inch  bars  spaced  18  inches.  No 
definite  calculation  can  be  made  for  the 
vertiqal  bars.  Bars  1  inch  thick  should  be 
spaced  36  inches  in  the  lower  part  and  |- 
inch  bars  in  the  upper  part.  The  founda- 
tion under  the  wall  should  be  made  2  feet 
wide  and  18  inches  deep  and  a  4-inch  slab 
used  for  the  floor, 

CONCRETE  WALKS 

Drainage  of  Foundations.  The  ex- 
cavation should  be  made  of  a  sufficient 
depth  to  get  below  the  frost  line.  The 
ground  should  be  tamped  thoroughly, 
and  the  excavation  filled  with  cinders, 
broken  stone,  gravel,  or  brickbat,  up 
to  within  four  inches  (or  whatever 
thickness  of  slab  is  to  be  used)  of  the 
top  of  the  grade.  The  foundation 


Fig.  53.     Section  of  Silo 


162  REINFORCED  CONCRETE 

should  be  thoroughly  rammed,  and  by  using  gravel  or  cinders 
to  make  this  foundation,  a  very  firm  surface  can  be  secured. 
Side  drains  should  be  put  in  at  convenient  intervals  where  out- 
lets can  be  secured.  The  foundation  is  sometimes  omitted,  even 
in  cold  climates,  if  the  soil  is  porous.  Walks  laid  on  the  natural 
soils  have  proved,  in  many  cases,  to  be  very  satisfactory. 

At  the  Convention  of  the  National  Cement  Users'  Associa- 
tion, held  at  Buffalo,  New  York,  in  1908,  the  Committee  on 
Sidewalks,  Streets,  and  Floors  presented  the  following  specifi- 
cations for  sidewalk  foundations: 

The  ground  base  shall  be  made  as  solid  and  permanent  as  possible. 
Where  excavations  or  fills  are  made,  all  wood  or  other  materials  which 
will  decompose  shall  be  removed,  and  replaced  with  earth  or  other 
filling  like  the  rest  of  the  foundation.  Fills  of  clay  or  other  material 
which  will  settle  after  heavy  rains  or  deep  frost  should  be  tamped, 
and  laid  in  layers  not  more  than  six  inches  in  thickness,  so  as  to  insure 
a  solid  embankment  which  will  remain  firm  after  the  walk  is  laid. 
Embankments  should  not  be  less  than  21  foet 
wider  than  the  walk  which  is  to  be  laid. 
When  porous  materials,  such  as  coal  ashes, 
granulated  slag,  or  gravel,  are  used,  under- 
drains  of  tile  should  be  laid  to  the  curb  drains 
or  gutters,  so  as  to  prevent  water  accumulat- 
ing and  freezing  under  the  walk  and  breaking 
the  block. 

Concrete  Base.     The  concrete  for  the 
base   of  walks  is  usually  composed   of 

1  part  Portland  cement,  3  parts  sand, 
Fig.  54.    Square  Tamper 

and  5  parts  stone  or  gravel.    Sometimes, 

however,  a  richer  mixture  is  used,  consisting  of  1  part  cement, 
2  parts  sand,  and  4  parts  broken  stone ;  but  this  mixture  seems 
to  be  richer  than  what  is  generally  required.  The  concrete 
should  be  thoroughly  mixed  and  rammed,  Fig.  54.  The  broken 
stone  or  gravel  should  not  be  larger  than  1  inch,  varying  down 
to  I  inch,  and  free  from  fine  screenings  or  soft  stone.  All 
stone  or  gravel  under  |  inch  is  considered  sand. 

The  thickness  of  the  concrete  base  depends  upon  the  location, 
the  amount  of  travel,  and  the  danger  of  being  broken  by  frost. 
The  usual  thickness  in  residence  districts  is  3  inches,  with  a 
wearing  thickness  of  1  inch,  making  a  total  of  4  inches,  Fig.  55. 


REINFORCED  CONCRETE 


163 


In  business  sections,  the  walks  vary  from  4  to  6  inches  in  total 
thickness,  in  which  the  finishing  coat  should  not  be  less  than 
1£  inches. 

The  lines  and  grades  given  for  walks  by  the  engineer  should 
be  carefully  followed.  The  mold  strips  should  be  firmly  blocked 
and  kept  perfectly  straight  to  the  height  of  the  grade  given. 
The  walks  usually  are  laid  with  a  slope  of  -I  inch  to  the  foot 
toward  the  curb. 

The  concrete  base  is  cut  into  uniform  blocks.  The  blocks  are 
usually  from  4  to  6  feet  square,  but  sometimes  they  are  made 
much  larger.  The  joints  made  by  cutting  the  concrete  should 
be  filled  with  dry  sand,  and  their  exact  location  marked  on  the 


Fig.  55.   Concrete  Sidewalk  and  Curb  NN  '/^ 

forms.  The  cleaver  or  spud  that  is  used  in  making  the, joints 
should  not  be  less  than  \  of  an  inch  or  over  £  of  an  inch  in 
thickness.  , 

Top  Surface.  The  wearing  surface  usually  consists  of  1 
part  Portland  cement  and  2  parts  crushed  stone  or  good,  coarse 
sand— all  of  which  will  pass  through  a  ^-inch  mesh  screen— 
thoroughly  mixed  so  that  a  uniform  color  is  secured.  This  mix- 
ture is  then  spread  over  the  concrete  base  to  a  thickness  of  one 
inch,  this  being  done  before  the  concrete  of  the  base  has  set 
or  become  covered  with  dust.  The  mortar  is  leveled  off  with  a 
straightedge,  and  smoothed  down  with  a  float  or  trowel  after 
the  surface  water  has  been  absorbed.  The  exact  time  at  which 
the  surface  should  be  floated  depends  upon  the  setting  of  the 
cement,  and  must  be  determined  by  the  workmen ;  but  the  final 
floating  is  not  usually  performed  until  the  mortar  has  been  in 


164 


REINFORCED  CONCRETE 


place  from  two  to  five  hours  and  is  partially  set.  This  final 
floating  is  done  first  with  a  wooden  float,  and  afterwards  with  a 
metal  float  or  trowel.  The  top  surface  is  then  cut  directly  over 
the  cuts  made  in  the  base,  care  being  taken  to  cut  entirely 
through  the  top  and  base  all  around  each  block.  The  joint  is 
then  finished  with  a  jointer,  Fig.  56,  and  all  edges  rounded  or 
beveled.  Caution  should  be  observed,  in  the  final  floating  or 
finishing,  not  to  overdo  it,  as  too  much  working  will  draw  the 
cement  to  the  surface,  leaving  a  thin  layer  of  neat  cement,  which 
is  likely  to  peel  off.  Just  before  the  floating,  a  very  thin  layer 
of  dryer,  consisting  of  dry  cement  and  sand  mixed  in  the  pro- 
portion of  1:1,  or  even  richer,  is  not  infrequently  spread  over 

the  surface;  but  this  is 
generally  undesirable, 
as  it  tends  to  make  a 
glossy  walk.  A  dot  roller 
or  line  roller,  Figs.  57 
and  58.  may  be  employed 
to  relieve  the  smoothness. 
At  the  meeting  of  the 
National  Cement  Users ' 
Association  already  re- 
ferred to,  the  Committee 
on  Sidewalks,  Floors, 
and  Streets  recom- 
mended the  following 
specifications  for  the  top 
coat: 

Three  parts  high-grade  Portland  cement  and  five  parts  clean,  sharp 
sand,  mixed  dry  and  screened  through  a  No.  4  sieve.  In  the  top  coat, 
the  amount  of  water  used  should  be  just  enough  so  that  the  surface  of 
the  walk  can  be  tamped,  struck  off,  floated,  and  finished  within  20 
minutes  after  it  is  spread  on  the  bottom  coat ;  and,  when  finished,  it 
should  be  solid  and  not  quaky. 

In  the  January,  1907,  number  of  Cement,  Mr.  Albert  Moyer, 
Assoc.  M.  Am.  Soc.  C.  E.,  in  discussing  the  subject  of  cement 
sidewalk  pavements,  gives  specifications  for  monolithic  slab  for 
paving  purposes,  and  as  an  example  of  this  construction,  he 
cites  the  pavement  around  the  Astor  Hotel,  New  York : 


Fig.  56.    Jointers 


REINFORCED  CONCRETE 


165 


As  an  alternative,  and  instead  of  using  a  top  coat,  make  one  slab  of 
selected  aggregates  for  base  .and  wearing  surface,  filling  in  between  the 
frames  concrete  flush  with  established  grade.  Concrete  to  be  of  selected 
aggregates,  all  of  which  will  pass  through  a  1-inch  mesh  sieve ;  hard, 
tough  stones  or  pebbles,,  graded  in  size ;  proportions  to  be  1  part 
cement,  2|  parts  crushed  hard  stone  screenings  or  coarse  sand,  all  pass- 
ing a  i-inch  mesh,  and  all  collected  on  a  4-inch  mesh.  Tamped  to  an 
even  surface,  prove  surface  with  straightedge,  smooth  down  with  float 
or  trowel ;  a  natural  finish  can  be  obtained  by  scrubbing  with  a  wire 
brush  and  water  while  concrete  is  "green,"  but  after  final  set. 

Seasoning.  During  the  setting  the  wearing  surface  must 
be  protected  from  the  rays  of  the  sun  by  a  covering  which  is 


Fig.  57.   Brass  Dot  Roller 

raised  a  few  inches  above  the  pavement  so  that  it  does  not  come 
in  contact  with  the  surface.  After  the  pavement  has  set  hard, 
sprinkle  freely  two  or  three  times  a  day  for  a  week  or  more. 

Cost.  The  cost  of  concrete  sidewalks  is  variable.  The 
construction  at  each  location  usually  requires  only  a  few  days7 
work;  but  the  time  and  expense  of  transporting  the  men.  tools, 
and  materials  make  an  important  item.  One  of  the  skilled 
workmen  should  be  in  charge  of  the  men,  so  that  the  expense 
of  a  foreman  will  not  be  necessary.  The  amount  of  walk  laid 
per  day  is  limited  by  the  amount  of  surface  that  can  be  floated 


166 


REINFORCED  CONCRETE 


and  troweled  in  a  day.  If  the  surfacers  do  not  work  overtime, 
it  will  be  necessary  to  stop  concreting  in  the  middle  of  the  after- 
noon, so  that  the  last  concrete  placed  will  be  in  condition  for 
finishing  during  the  regular  working  hours.  The  work  of  con- 
creting may  be  continued  considerably  later  in  the  afternoon  if 
a  drier  concrete  is  used  in  mixing  the  top  coat,  and  only  enough 
water  is  used  so  that  the  surface  can  be  floated  and  finished  soon 
after  being  placed.  The  men  who  have  been  mixing,  placing, 
and  ramming  concrete  can  complete  their  day's  work  by  pre- 
paring and  ramming  the  foundations  for  the  next  day's  work. 


Fig.  58.    Brass  Lino  Roller 

The  contract  price  for  a  well-constructed  sidewalk  4  to  5 
inches  in  thickness,  with  a  granolithic  finish,  will  vary  from 
15  cents  to  30  cents  per  square  foot. 

CONCRETE  CURB 

The  curb  is  usually  built  just  in  advance  of  the  sidewalk. 
The  foundation  is  prepared  similarly  to  that  of  walks ;  the  curb 
is  divided  into  lengths  similar  to  that  of  the  walk ;  and  the  joints 
between  the  blocks,  and  also  between  the  walk  and  the  curb,  are 
made  similar  to  the  joints  between  the  blocks  of  the  walk.  The 


REINFORCED  CONCRETE 


167 


concrete  is  generally  composed  of  1  part  Portland  cement,  3 
parts  sand,  and  5  parts  stone,  although  a  richer  mixture  is 
sometimes  used.  A  fac- 
ing of  mortar  or  grano- 
lithic finish  on  the  ex- 
posed part  will  improve 
the  wearing  qualities  of 
the  curb. 

Types.  There  are 
two  general  types  of 
curb  used— a  curb  rec- 
tangular in  section,  and  FiS-  59-  TyPical  Curb  Sections 
a  combined  curb  and  gutter;  the  two  types  are  shown  in  Fig.  59. 
The  foundations  for  both  are  constructed  alike.  Both  kinds  of 
curb  are  made  in  place  or  are  molded  and  set  in  place  like  stone 
curb,  but  the  former  method  is  pref- 
erable. A  metal  corner  is  some- 
times laid  in  the  exposed  edge  of 
the  curb  to  protect  it  from  wear. 

Construction.  The  construction 
of  the  rectangular  section  is  a 
simple  process,  but  requires  care. 
The  section  is  usually  about  7  inches 
wide  and  from  20  to  30  inches  deep. 
After  the  foundation  has  been  prop- 
erly prepared,  the  forms  are  set  in 
place.  Fig.  60  shows  the  section  of 
a  curb  7  inches  wide  and  24  inches 
deep,  and  the  forms  as  they  are 
often  used.  The  forms  for  the  front 
and  back  both  consist  of  three 
planks  1|  inches  thick  and  8  inches 
wide,  and  are  surfaced  on  the  side 
next  the  concrete.  They  are  held  in 
place  at  the  bottom  by  the  two  2-  by 
4-inch  stakes,  which  at  the  top  are 
kept  from  spreading  by  a  clamp. 


Fig.  60.    Forms  for  Con- 
structing Curb 


168 


REINFORCED  CONCRETE 


Fig.  61.    CurbEdger 


A  sheet-iron  plate  |  inch  thick  is  inserted  every  6  feet,  or  at 
whatever  distance  the  joints  are  made.    After  the  concrete  has 

been  placed  and 
rammed,  and  has  set 
hard  enough  to  sup- 
port itself,  the  plate 
and  front  forms  are 
removed,  and  the  sur- 
face and  top  are  fin- 
ished smooth  with  a 
trowel,  and  with  other 
tools  such  as  shown  in 
Figs.  61, .  62,  and  63. 
The  joint  is  usually  plastered  over,  and  acts  as  an  expansion 
joint.  The  forms  on  the  back  are  not  removed  until  the  con- 
crete is  well  set.  If  a 
mortar  or  granolithic 
finish  is  used,  a  piece 
of  sheet  iron  is  placed 
in  the  form  one  inch 
from  the  facing;  the 

mortar   is   placed   be- 

Fig.  62.    Radius  Tool 
tween    the    sheet   iron 

and  the  front  form,  and  the  coarser  concrete  is  placed  back  of 
the  sheet  iron,  Fig.  64.    The  sheet  iron  is  then  withdrawn  and 

the  two  concretes  thor- 
oughly tamped. 

Fig.  64  shows  the 
section  of  a  combined 
curb  and  gutter,  and 
the  forms  that  are  nec- 
essary for  its  construc- 
tion. This  combination 

is  often  laid  with  fair 
Fig.  63.    Inside  Angle  Tool  ,,  ., 

results  on  a  porous  soil 

without  any  special  foundation.    A  If-inch  plank  12  inches 
wide  is  used  for  the  back  form,  and  is  held  in  place  at  the  bottom 


REINFORCED  CONCRETE 


169 


by  pegs.  The  front  form  consists  of  a  plank  1|  by  6  inches,  and 
is  held  in  place  by  pegs.  Before  the  concrete  is  placed,  two 
sheet-iron  plates,  cut  as  shown  in  the  figure,  are  inserted  in  the 
forms,  6  feet  to  8  feet  apart.  After  the  concrete  for  the  gutter 
and  the  lower  part  of  the  curb  is  placed  and  rammed,  a  l|-inch 
plank  is  fixed  against  these  plates  and  held  there  by  screw 
clamps,  Fig.  64.  The  upper  part  of  the  curb  is  then  molded. 
When  the  concrete  is  set  sufficiently  to  stay  in  place,  the  front 
forms  and  plates  are  removed,  and  the  surface  is  treated  in  the 
same  manner  as  described  for  the  other  type  of  curb. 


Fig.  64.    Forms  for  Curb  and  Gutter 

Cost.  The  cost  of  concrete  curb  will  depend  upon  the  con- 
ditions under  which  it  is  made.  In  ordinary  circumstances,  the 
contract  price  will  be  about  60  cents  per  lineal  foot  for  rectan- 
gular curbing  6  inches  wide  and  24  inches  deep;  or  80  cents  per 
lineal  foot  for  curbing  8  inches  wide  and  24  inches  deep.  Under 
favorable  conditions  on  large  jobs,  6-inch  curbing  can  be  con- 
structed for  40  cents  or  45  cents  per  lineal  foot.  These  prices 
include  the  excavation  that  is  required  below  the  street  grade. 

The  cost  of  the  combined  curb  and  gutter  is  about  10  to  20 
per  cent  more  than  that  of  the  rectangular  curbing.  In  addition 
to  having  a  larger  surface  to  finish,  the  combined  curb  and 
gutter  requires  more  material,  and  therefore  more  work  to 
construct  it. 


170  REINFORCED  CONCRETE 

CONCRETE  CONSTRUCTION  WORK 
MACHINERY  FOR  CONCRETE  WORK 

Concrete  Plant.  No  general  rule  can  be  given  for  laying 
out  a  plant  for  concrete  work.  Every  job  is,  generally,  a  prob- 
lem by  itself  and  requires  a  careful  analysis  to  secure  the  most 
economical  results.  .  Since  it  is  much  easier  and  cheaper  to 
handle  the  cement,  sand,  and  stone  before  they  are  mixed,  the 
mixing  should  be  done  as  near  the  point  of  installation  as  pos- 
sible. All  facilities  for  handling  the  materials,  charging  the 
mixer,  and  distributing  the  concrete  after  it  is  mixed  must  be 
established  and  maintained.  The  charging  and  distributing  are 
often  done  by  wheelbarrows  or  carts,  and  economy  of  operation 
depends  largely  upon  system  and  regularity  of  operation.  Sim- 
ple cycles  of  operations,  the  maintenance  of  proper  runways, 
together  with  clocklike  regularity,  arc  necessary  for  economy. 
To  shorten  the  distance  of  wheeling  the  concrete,  it  is  very  often 
found,  on  large  buildings,  better  to  have  two  medium-sized 
plants  located  some  distance  apart,  than  to  have  one  large  plant. 

The  design  of  a  plant  for  handling  the  material  and  concrete 
and  the  selection  of  a  mixer  depend  upon  local  conditions,  the 
amount  of  concrete  to  be  mixed  per  day,  and  the  total  amount 
required  on  the  contract.  It  is  evident  that  on  large  jobs  it  pays 
to  invest  a  considerable  sum  in  machinery  to  reduce  the  number 
of  men  and  horses.  Even  on  small  jobs,  where  only  10  to  15 
cubic  yards  are  to  be  mixed  daily,  it  is  better  to  use  a  mixer  than 
mix  the  concrete  by  hand.  Mixers  are  now  made  in  very  small 
sizes,  some  having  a  capacity  of  only  6  or  8  cubic  feet.  Some 
of  larger  sizes  have  a  capacity  of  2  to  3  cubic  yards. 

Concrete  Mixers 

Types.  The  best  concrete  mixer  is  the  one  that  turns  out 
the  maximum  of  thoroughly  mixed  concrete  at  the  minimum  of 
cost  for  power,  interest,  and  maintenance.  The  type  of  mixer 
with  a  complicated  motion  gives  better  and  quicker  results  than 
one  with  a  simpler  motion.  There  are  two  general  classes  of 
concrete  mixers— continuous  mixers  and  batch  mixers.  A  con- 


REINFORCED  CONCRETE 


171 


tinuous  mixer  is  one  into  which  the  materials  are  fed  constantly, 
and  from  which  the  concrete  is  discharged  constantly.  Batch 
mixers  are  constructed  to  receive  the  cement  with  its  propor- 
tionate amount  of  sand  and  stone,  all  at  one  charge,  to  mix 
these  ingredients,  and  then  to  discharge  them  in  a  mass.  No 


Fig.  65.    Ransome  Gasoline-Driven  Concrete  Mixing  Outfit  with   Fixed 

Batch  Hopper.    Discharge  Chute  in  Position  for  Mixing 
Courtesy  of  Ransome  Concrete  Machinery  Company,  Chicago,  Illinois 

very  distinct  line  can  be  drawn  between  the  two  classes,  for 
many  of  these  mixers  are  adapted  to  either  continuous  or  batch 
mixing.  Usually,  batch  mixers  are  preferred,  as  it  is  very 
difficult  to  feed  the  mixers  uniformly  unless  the  materials  are 
measured. 

Continuous  Mixers.     These  usually  consist  of  a  long  screw  or 
pug  mill  that  pushes  the  materials  along  a  drum  until  they  are 


172  REINFORCED  CONCRETE 

discharged  in  a  continuous  stream  of  concrete.  Where  the 
mixers  are  fed  with  automatic  measuring  devices,  the  concrete 
is  not  regular,  as  there  is  no  reciprocating  motion. 

Batch  Mixers.  Batch  mixers  differ  somewhat  in  their  details ; 
but  in  general  they  have  a  drum,  double  cone,  or  a  cubical  box 
of  steel  which  is  usually  fitted  up  inside  with  deflector  blades. 
There  is  a  great  variety  of  these  mixers  on  the  market. 

Fig.  65  represents  a  Ransome  mixer,  which  is  a  batch  mixer. 
The  concrete  is  discharged  after  it  is  mixed,  without  tilting  the 
body  of  the  machine.  The  mixer  revolves  continuously,  even 
while  the  concrete  is  being  discharged.  Riveted  to  the  inside 
of  the  drum  are  a  number  of  steel  scoops  or  blades.  These 
scoops  pick  up  the  material  in  the  bottom  of  the  mixer,  and,  as 
the  latter  revolves,  carry  the  material  upward  until  it  slides 
out  from  them. 

Sources  of  Power.  General  Considerations.  One  essential 
point  that  must  always  be  considered  is  the  source  of  power  for 
operating  the  mixer,  conveyors,  hoists,  derricks,  and  cableways. 
If  it  is  possible  to  run  the  machinery  by  electricity,  it  is  often 
economical  to  do  so,  but  this  will  depend  a  great  deal  upon  the 
local  price  for  electricity. 

Steam  Engines.  When  all  the  machinery  can  be  supplied 
with  steam  from  one  centrally  located  boiler,  this  arrangement 
will  be  found,  perhaps,  the  most  efficient.  A  vertical  steam 
engine  is  generally  used  to  operate  the  mixer.  The  smaller 
sizes  of  engines  and  mixers  are  mounted  on  the  same  frame; 
but  on  account  of  the  weight  it  is  necessary  to  mount  the  larger 
sizes  on  separate  frames. 

Upright  tubular  boilers  are  generally  used  to  supply  steam 
for  concrete  mixers  and  hoists  operated  by  steam  engines  when 
they  are  isolated.  For  the  smaller  sizes  of  mixers,  the  boilers 
are  mounted  on  the  same  frame  as  the  engine  and  mixer. 

Gasoline  Engines.  Gasoline  engines  are  used  to  some  extent 
to  operate  concrete  mixers.  Thus  far  they  have  been  limited 
chiefly  to  portable  plants  such  as  are  employed  for  street  work. 
The  fuel  for  the  gasoline  engine  is  much  more  easily  moved 
from' place  to  place  than  the  fuel  for  a  steam  engine. 


REINFORCED  CONCRETE  173 

There  are  two  types  of  gasoline  engines— the  horizontal  and 
the  vertical.  The  vertical  engines  occupy  much  less  floor  space 
for  a  given  horsepower  than  the  horizontal.  Both  are  types  of 
the  engines  commonly  known  as  four-cycle  engines.  In  the 
operation  of  them,  four  strokes  of  the  piston  are  required  to 
draw  in  a  charge  of  fuel,  compress  and  ignite  it,  and  discharge 
the  exhaust  gases.  The  quantity  of  gasoline  consumed  in  10 
hours  is,  on  the  average,  about  1  gallon  for  each  rated  horse- 
power for  any  given  size  of  engine.  At  15  cents  per  gallon  for 
gasoline,  the  hourly  expense  per  horsepower  will  be  1.5  cents. 

Hoisting  and  Transporting  Equipment 

General  Types.  When  the  concrete  requires  hoisting,  this 
is  done  sometimes  by  the  same  engine  that  is  used  in  mixing  the 
concrete,  but  it  is  generally  considered  better  practice  on  large 
buildings  to  have  a  separate  engine  to  do  the  hoisting.  If  it  is 
possible  to  use  a  standard  hoist,  it  is  usually  economical  to  do  so. 
These  hoists  are  equipped  with  automatic  dump  buckets. 

A  standard  double-cylinder,  double-friction-drum  hoisting 
engine  is  designed  to  fulfil  the  requirements  of  a  general  con- 
tractor for  all  classes  of  derrick  work  and  hoisting.  Steam  can 
be  supplied  from  a  separate  boiler,  or  from  a  boiler  that  sup- 
plies various  engines  with  steam.  The  double-friction  drums 
are  independent  of  each  other;  therefore,  if  desired,  one  or  two 
derricks  can  be  handled  at  the  same  time.  The  hoist  is  fitted 
with  ratchets  and  pawls,  and  winch  heads  attached  to  the  end 
of  each  drum  shaft.  The  winch  heads  can  be  used  for  any 
hoisting  or  hauling  desired,  independent  of  the  drums. 

Advantages  of  Electric  Power.  Very  often  the  cycle  of 
operation  of  a  hoist  is  of  an  intermittent  character.  The  power 
required  is  at  a  maximum  only  a  part  of  the  time,  even  though 
the  hoist  may  be  operated  practically  continuously.  From  an 
economical  point  of  view,  these  conditions  give  the  electric- 
motor-driven  hoist  special  advantages,  in  that  the  electric  hoist 
is  always  ready,  but  uses  power  only  when  in  actual  operation, 
and  then  only  in  proportion  to  the  load  handled.  The  ease  with 
which  a  motor  is  moved,  and  the  simplicity  of  the  connection 


174 


REINFORCED  CONCRETE 


to  the  service  supply — requiring  only  that  two  wires  be  con- 
nected—are also  in  favor  of  the  electric  motor. 

Hoisting  Lumber  and  Steel.  In  constructing  large  rein- 
forced concrete  buildings,  usually  a  separate  hoist  is  used  to 
elevate  the  steel  and  the  lumber  for  the  forms.  It  may  be 
equipped  with  either  an  electric  motor  or  an  engine,  depending 
upon  the  general  arrangement  of  the  plant.  These  hoists  are 
usually  of  the  single-drum  type. 

Hoisting  Concrete.  In  building  construction,  concrete  is 
usually  hoisted  in  automatic  dumping  buckets,  one  of  which  is 

illustrated  in  Fig.  66. 
The  bucket  is  designed  to 
slide  up  and  down  a  light 
framework  of  timber,  as 
shown  in  Fig.  67,  and  to 
dump  automatically  when 
it  reaches  the  proper 
place.  The  dumping  of 
the  buckets  is  accom- 
plished by  the  bucket's 
pitching  forward  at  the 
point  where  the  front 
guide  in  the  hoisting 
tower  is  cut  off ;  the  bucket 

Ransconcretest  Buckete  £or        rights  itself  automatically 
Courtesy   of   Ransome    Concrete   Machin-    as    soon    as    it    begins    to 
cry  Company,  Chicago,  Illinois.  degcend>       These    buckets 

are  often  used  for  hoisting  sand  and  stone  as  well  as  concrete. 
Their  capacity  varies  from  10  cubic  feet  to  40  cubic  feet. 

Charging  Mixers.  The  mixers  are  usually  charged  by 
means  of  wheelbarrows,  although  other  means  are  sometimes 
used.  The  capacity  of  the  wheelbarrows  varies  from  2  cubic 
feet  to  4  cubic  feet,  the  former  size  being  the  more  general  one, 
though  with  good  runways  a  man  can  handle  4  cubic  feet  of 
stone  or  sand  in  a  well-constructed  wheelbarrow. 

In  Fig.  68  is  shown  an  automatic  loading  bucket  which  has 
been  devised  by  the  Koehring  Machine  Company  for  charging 


Fig. 


REINFORCED  CONCRETE 


175 


the  mixers  made  by  them.  The 
bucket  is  operated  by  a  friction 
clutch,  and  is  provided  with  an 
automatic  stop.  Wheelbarrows 
may  be  used  in  charging  the 
buckets,  unless  the  materials 
are  close  to  the  mixer. 

Transporting  Mixed  Con- 
crete. Concrete  is  usually 
transported  by  wheelbarrows, 
carts,  cars,  or  derricks,  although 
other  means  are  frequently  em- 
ployed. It  is  essential,  in 
handling  or  transporting  con- 
crete, that  care  be  taken  to  pre- 
vent the  separation  of  the  stone 
from  the  mortar.  With  a  dry 
mixture,  there  is  not  so  much 
danger  of  the  stone  separating 
as  with  a  wet  mixture.  Owing 
to  the  difference  in  the  time  of 
setting  of  Portland  cement  and 
natural  cement,  the  former  can 
be  conveyed  much  farther  and 
with  less  danger  of  the  initial 
setting  taking  place  before  the 
concrete  is  deposited. 

Concrete  Plant  for  Street 
Work.  A  self-propelling  mix- 
ing and  spreading  machine  has 
been  found  very  desirable  for 
laying  concrete  base  for  street 
pavements.  A  plant  of  this 
kind,  which  has  been  devised  by 
the  Municipal  Engineering  and 
Contracting  Company,  may  be 
described  as  follows: 


SECTFOH  FT- ft 
Fig.  67.     Details  of  Hoisting 
Tower 


176  REINFORCED  CONCRETE 

The  mixer  is  of  the  improved  cube  type,  mounted  on  a  heavy 
truck  frame.  The  concrete  is  discharged  into  a  specially  de- 
signed bucket,  which  receives  the  whole  batch  and  travels  to 
the  rear  on  a  truck  about  25  feet  long.  The  head  of  the  truck 
is  supported  by  guys,  and  also  by  a  pair  of  small  wheels  near 
the  middle  of  the  truck,  which  rest  on  the  graded  surface  of  the 
street.  The  truck  or  boom  is  pivoted  at  the  end  connected  to  the 


Fig.  68.     Koehring  Steam-Driven  Concrete  Mixer  with  Side  Loader  and 

Water  Measuring  Tank 
Courtesy   of    Koehring    Machine    Company,    Milwaukee,    Wisconsin 

main  truck,  and  has  a  horizontal  swing  of  about  170  degrees,  so 
that  a  street  50  feet  wide  is  covered.  An  inclined  track  is  also 
constructed,  on  which  a  bucket  for  elevating  and  charging  the 
mixer  is  operated.  The  bucket  is  loaded  while  resting  on  the 
ground,  with  the  proper  ingredients  for  a  batch,  from  the  mate- 
rials that  have  been  distributed  in  piles  along  the  street.  The 
bucket  is  then  pulled  up  the  incline,  and  the  contents  dumped 
into  the  mixer.  An  automatic  water-measuring  supply  tank, 


REINFORCED  CONCRETE 


177 


mounted  on  the  upper  part  of  the  frame,  insures  a  uniform 
amount  of  water  for  each  batch  mixed.  Power  for  hoisting, 
mixing,  and  distributing  the  concrete,  and  propelling  the  ma- 
chine is  furnished  by  a  16-horsepower  gasoline  engine  of  the 
automobile  type.  The  machine  can  be  moved  backward  as  well 
as  forward,  and  is  supplied  with  complete  steering  gear. 

Machinery  for  Miscellaneous  Operations 

Concrete-Block  Machines.  There  are  two  general  types  of 
hpllow-concrete-block  machines  on  the  market — those  with  a 
vertical  face  and  those  with  a  horizontal  face.  In  making  blocks 


Fig:,  69.     Hercules  Cement  Stono  ^Machine 
I?  ,'  Courtesy 'qf  Centu,ry  Cement.  Company,  JlocUe^ter^  ,Areto  York 

with  the  vertical-faced  machine,  the  face  of  the  block  is  in  a 
vertical  position  when  molded,  and  the  block  is  simply  lifted 
from  the  machine  on  its  base  plate.  In  the  horizontal-faced 
type  of  block  machine,  the  block  is  made  with  the  face  down,  the 
face-plate  forming  the  bottom  of  the  mold.  The  cores  are 
withdrawn  horizontally,  or  the  mold  is  turned  over  and  the  core 
is  taken  out  vertically;  the  block  is  then  ready  for  removal. 
The  principal  difference  in  the  two  types  of  machine  is  that,  if 
a  special  facing  is  desired  on  the  block,  it  is  more  convenient  to 
do  that  with  a  horizontal-faced  machine.  With  the  vertical- 
faced  machine,  the  special  facing  is  put  on  by  the  use  of  a 
parting-plate.  When  the  parting-plate  is  removed,  the  two 


178 


REINFORCED  CONCRETE 


mixtures  of  concrete  are  bonded  together  by  tamping  the  coarser 
material  into  the  facing  mixture. 

Fig.  69  shows  a  Hercules  machine.  The  foundation  parts 
can  be  attached  for  making  any  length  of  block  up  to  6  feet. 
The  illustration  shows  two  molds  of  different  lengths  attached. 
These  machines  are  constructed  of  iron  and  steel,  except  that 
the  pallets  (the  plates  on  which  the  blocks  are  taken  from  the 
machine)  may  be  either  wood  or  steel.  This  type  of  machine 
is  the  horizontal,  or  face-down,  machine. 


Fig.    70.     Blocks   Made   on    Hercules    Machine 

In  Fig.  70  are  shown  a  group  of  the  various  forms  which  may 
be  made.  The  figure  also  illustrates  the  ornamental  possibilities 
of  concrete-block  construction. 

Fig.  71  pictures  a  Hobbs  face-down,  wet-process  block  ma- 
chine. The  front  and  sides  of  the  machine  can  be  let  down, 
thus  facilitating  the  removal  of  the  blocks.  The  cores  are 
shown  withdrawn  in  the  figure. 

Cement-Brick  Machines.  Fig.  72  shows  a  machine  for 
making  cement  brick.  Ten  bricks,  2|  by  3|  by  8  inches,  are 
made  at  one  operation.  By  using  a  machine  in  which  the  bricks 


REINFORCED  CONCRETE 


179 


are  made  on  the  side,  a  wetter  mixture  of  concrete  can  be  used 
than  if  they  are  made  on  the  edge.  The  concrete  usually  con- 
sists of  a  mixture  of  1  part  Portland  cement  and  4  parts  sand. 
The  curing-  of  these  bricks  is  the  same  as  that  for  concrete 
blocks.  In  making-  the  bricks,  a  number  of  wood  pallets  are 
required,  as  the  brick  should  not  be  removed  from  the  pallet 
until  the  concrete  has  set  and  the  bricks  are  ready  to  use. 


Fig.  71.    Hobbs  Face-Down,  Wet-Process  Con- 
crete Block  Machine 

Courtesy  of  Ho'b'bs  Concrete  Machinery  Com- 
pany, Detroit,  Michigan 

Sand- Washing.  Since  dirty  sand  can  be  easily  obtained 
while  clean  sand  can  be  secured  only  at  high  cost,  it  sometimes 
becomes  necessary  to  use  dirty  sand  and  to  wash  it.  If  only  a 
small  quantity  is  to  be  washed,  it  may  be  done  with  a  hose.  A 
trough  should  be  built  about  8  feet  wide  and  15  feet  long,  the 
bottom  having  a  slope  of  about  19  inches  in  its  entire  length. 
The  sides  should  be  approximately  8  inches  high  at  the  lower 
end,  and  increase  gradually  to  a  height  of  perhaps  36  inches  at 
the  upper  end.  In  the  lower  end  of  the  trough  there  should  be 


180  REINFORCED  CONCRETE 

a  gate  about  6  inches  high,  sliding  in  guides  so  that  it  can  be 
easily  removed.  The  sand  is  placed  in  the  upper  end  of  the 
trough,  and  a  stream  of  water  is  played  on  it.  The  sand  and 
water  flow  down  the  trough,  and  the  dirt  passes  over  the  gate 
with  the  overflow  water.  With  a  trough  of  the  above  dimen- 
sions, and  a  stream  of  water  from  a  t-inch  hose,  3  cubic  yards 
of  sand  should  be  washed  in  an  hour. 

Concrete  mixers  are  often  used  for  washing  sand.  The  sand 
is  dumped  into  the  mixer  in  the  usual  manner  and  the  water  is 

turned  on.  When  the 
mixer  is  filled  with  water 
so  that  it  overflows  at 
the  discharge  end,  the 
mixer  is  started.  The 
revolving  of  the  mixer 
enables  the  water  to  sep- 
arate the  dirt  from  the 
sand,  and  the  dirt  is 
carried  off  by  the  over- 
Fig.  72.  Century  Cement  Brick  Machine  fl°W  °f  Water'  When 

the  water  runs  clear,  the 

washing  is  complete  and  the  sand  is  dumped  in  the  usual  way. 
If  large  quantities  of  sand  require  washing  special  machinery 
for  that  purpose  should  be  employed. 

FORMS 
Building  Forms 

General  Requirements.  In  actual  construction  work,  the 
cost  of  forms  is  a  large  item  of  expense  and  offers  the  best  field 
for  the  exercise  of  ingenuity.  For  economical  work,  the  design 
should  consist  of  a  repetition  of  identical  units;  and  the  forms 
should  be  so  devised  as  to  require  a  minimum  of  nailing  to  hold 
them,  and  of  labor  to  make  and  handle  them.  In  constructing 
a  factory  building  of  two  or  three  stories,  usually  the  same  set 
of  forms  is  used  for  the  different  floors;  but  when  the  building 
is  more  than  four  stories  high,  two  or  more  sets  of  forms  are 
specified,  so  as  always  to  have  one  set  of  forms  ready  to  move. 


REINFORCED  CONCRETE  181 

Forms  are  constructed  of  the  cheaper  grades  of  lumber.  To 
secure  a  smooth  surface,  the  planks  are  planed  on  the  side  on 
which  the  concrete  will  be  placed.  Green  lumber  is  preferable 
lo  dry,  as  it  is  less  affected  by  wet  concrete.  If  the  surface  of 
the  planks  that  is  placed  next  to  the  concrete  is  well  oiled,  the 
planks  can  be  taken  down  much  more  easily,  and,  if  kept  from 
the  sun,  they  can  be  used  several  times.  Crude  oil  is  an  excel- 
lent and  cheap  material  for  greasing  forms,  and  it  can  be 
applied  with  a  whitewash  brush.  The  forms  should  be  oiled 
every  time  they  are  used.  The  object  is  to  fill  the  pores  of  the 
wood  rather  than  to  cover  it  with  a  film  of  grease.  Thin  soft 
soap,  or  a  paste  made  from  soap  and  water,  is  also  used. 

The  forms  should  be  so  tight  as  to  prevent  the  water  and 
thin  mortar  from  running  through  and  thus  carrying  off  the 
cement.  This  is  accom- 
plished  by  means  of 
tongued-and-grooved  or 

hovplpfl  prlop  hnirrU  Fi°'  73>  TyPlcal  Form  of  Construction 
OC\eiea-eage  oar  as,  Showing  Tongued-and-Grooved  and 

Fig.  73;  but  it  is  often  Beveled-Edge  Boards 

possible  to  use  square  lumber,  if  that  is  wet  thoroughly  so  as 
to  swell  it  before  the  concrete  is  placed.  The  beveled-edge 
boards  are  often  preferred  to  tongued-and-grooved  boards,  as 
(he  edges  tend  to  crush  as  the  boards  swell,  and  beveling  pre- 
vents buckling. 

Lumber  for  forms  may  be  made  of  1-inch,  IJ-inch,  or  2-inch 
plank.  The  spacing  of  studs  depends  in  part  upon  the  thickness 
of  concrete  to  be  supported,  and  in  part  upon  the  thickness  of 
the  boards  on  which  the  concrete  is  placed.  The  size  of  the 
studding  depends  upon  the  height  of  the  wall  and  the  amount  of 
bracing  used.  Except  in  very  heavy  or  high  walls,  2-  by  4-inch 
or  2-  by  6-inch  studs  are  used.  For  ordinary  floors  with  1-inch 
plank,  the  supports  should  be  placed  about  2  feet  apart;  with 
li-inch  plank,  3  feet  apart;  and  with  2-inch  plank,  4  feet  apart. 

The  length  of  time  required  for  concrete  to  set  depends  upon 
the  weather,  the  consistency  of  the  concrete,  and  the  strain 
which  is  to  come  on  it.  In  good  drying  weather,  and  for  very 
light  work,  it  is  often  possible  to  remove  the  forms  in  12  to  24 


182 


REINFORCED  CONCRETE 


hours  after  placing  the  concrete,  if  there  is  no  load  placed  on 
it.  The  setting  of  concrete  is  greatly  retarded  by  cold  or  wet 
weather.  Forms  for  concrete  arches  and  beams  must  be  left  in 
place  longer  than  forms  in  wall  work,  because  of  the  tendency 
to  fail  by  rupture  across  the  arch  or  beam.  In  small,  circular 
arches,  like  sewers,  the  forms  may  be  removed  in  18  to  24  hours, 


Fig.  74.     Forms  for  Columns.      (A)   Common  Method 
of  Construction  ;  (B)  Method  in  Construct- 
ing Harvard  University  Stadium 

if  the  concrete  is  mixed  dry ;  but  if  wet  concrete  is  used,  in  24 
to  48  hours.  Forms  for  large  arch  culverts  and  arch  bridges  are 
seldom  taken  down  in  less  than  28  days.  The  minimum  time  for 
the  removal  of  forms  should  be: 

For  bottom  of  slabs  and  sides  of  beams  and  girders,  7  days  ;  for 
bottom  of  beams  and  girders,  14  days ;  for  columns,  4  days  ;  for  walls, 
not  loaded,  1  to  2  days  ;  for  bridge  arches,  28  days. 


REINFORCED  CONCRETE 


183 


The  concrete  should  be  thoroughly  examined  before  any 
forms  are  removed.  Forms  must  be  taken  down  in  such  a  way 
as  not  to  deface  the  structure  or  to  disturb  the  remaining 
supports. 

Forms  for  Columns.  Column  forms  for  buildings  should 
be  so  constructed  that  they  will  support  the  ends  of  the  girders 
and  beam  forms  and  also  so  that  they  can  be  taken  down  before 
either  the  girder  or  beam  forms.  A  pocket  should  be  left  at 
the  bottom  so  that  they  may  be  cleaned  out  before  any  concrete 
is  poured. 

Fig.  74- A  shows  the  common  way,  or  some  modification  of  it, 
.of  constructing  forms  for  columns.  The  plank  may  be  1  inch, 
1£  inches,  or  2  inches  thick ;  and  the  cleats  are  usually  1  by  4 
inches  and  2  by  4  inches.  The  spacing  of  the  cleats  depends  on 
the  size  of  the  columns  and  the  thickness  pf  the  vertical  plank. 


Fig.  75.    Forms  for  Beams  and  Slabs 


Fig.  74- B  shows  column  forms  similar  to  those  used  in  con- 
structing the  Harvard  University  stadium.  The  planks  forming 
each  side  of  the  column  are  fastened  together  by  cleats,  and  then 
the  four  sides  are  fastened  together  by  slotted  cleats  and  steel 
tie-rods.  These  forms  can  be  quickly  and  easily  removed. 

Round  columns  are  often  desired  for  the  interior  columns  of 
buildings.  For  such  columns  it  is  generally  cheaper  and  more 
satisfactory  to  use  steel  forms. 

Forms  for  Beams  and'  Slabs.  A  very  common  style  of 
form  for  beam  and  slab  construction  is  shown  in  Fig.  75.  The 
size  of  the  different  members  of  the  forms  depends  upon  the 
size  of  the  beams,  the  thickness  of  the  slabs,  and  the  relative 


184 


REINFORCED  CONCRETE 


spacing  of  some  of  the  members.  If  the  beam  is  10  by  20 
inches,  and  the  slab  is  4  inches  thick,  then  1-inch  plank  sup- 
ported by  2-  by  6-inch  timbers  spaced  2  feet  apart  will  support 
the  slab.  The  sides  and  bottom  of  the  beams  are  enclosed  by 
IJ-inch  or  2-inch  plank  supported  by  3-  by  4-inch  posts  spaced 
4  feet  apart. 

Forms  for  fireproofing  I-beams  and  supporting  a  reinforced 
concrete  slab  are  generally  made  the  same  as  those  for  rein- 
forced concrete  slabs,  beams,  and  girders,  except  that  the  forms 
are  suspended  from  the  structural  steel  work  instead  of  being 
supported  on  posts,  Fig.  76. 

/» 

Top  of  Slab' 

-Heavy  Wire 


Fig.  76.     Forms  for  Fireproofing  I-Beams  and  Supporting  Concrete  Slab 

Cost  of  Forms.  There  are  several  items  that  enter  into 
the  cost  of  form  work,  the  principal  ones  being  the  cost  of  the 
lumber,  the  number  of  times  that  it  can  be  used,  and  the  cost 
of  labor  for  making,  erecting,  taking  down  thq§  forms,  and 
rebuilding  them  in  another  location. 

For  slab  forms  on  I-beams  about  1£  feet  of  lumber  are  re- 
quired per  square  foot  of  floor.  The  total  cost  per  square  foot 
of  floor  for  forms,  under  ordinary  conditions,  will  vary  from 
8  cents  to  11  cents. 

For  typical  reinforced  concrete  buildings  with  slabs,  beams, 
girders,  and  columns,  the  cost  for  forms  will  vary  from  9  cents 
to  12  cents  per  square  foot  of  surface  to  be^covered.  These 


REINFORCED  CONCRETE 


185 


surfaces  include  bottom  of  slab,  sides  and  bottoms  of  all  beams 
and  girders,  and  sides  of  all  columns. 

Forms  for  Sewers  and  Walls 

Forms  for  Conduits  and  Sewers.  Forms  for  conduits  and 
sewers  must  be  strong  enough  not  to  give  way,  or  to  become 
deformed,  while  the  concrete  is  being  placed  and  rammed ;  and 
they  must  be  rigid  enough  not  to  warp  from  being  alternately 
wet  and  dry.  They  must  be  constructed  so  that  they  can  readily 
be  put  up  and  taken  down,  and  can  be  used  several  times  on  the 
same  job.  The  interior  of  the  sewer  or  conduit  must  have 
a  smooth  and  even  fin- 
ish. This  has  usually 
been  done  by  covering 
the  forms  with  light- 
weight sheet  iron. 

These  forms  are  usu- 
ally built  in  lengths  of 
16  feet,  with  one  center 
at  each  end,  and  with 
three  to  five— depending 
on  the  size  of  the  sewer 
or  conduit— intermediate 
centers  in  the  lengths 
of  15  feet.  The  planks 
of  these  forms  are  made  Fig"  77'  Center  for  Round  Sewer 

of  2-  by  4-inch  material,  surfaced  on  the  outer  side,  with  the 
edge  beveled  to  the  radius  of  the  conduit.  The  ribs  are  bolted 
together,  and  are  held  by  wood  ties  2  by  4  or  2  by  6  inches. 

Forms  of  Torresdale  Filters.  In  constructing  the  Torres- 
dale  filters  for  supplying  Philadelphia  with  water,  several  large 
sewers  and  conduits  were  built  of  concrete  and  reinforced  with 
expanded  metal.  In  section,  the  sewers  were  round  and  the 
conduits  were  horseshoe-shaped,  with  a  comparatively  flat  bot- 
tom. The  sewers  were  6  feet  and  8  feet  6  inches,  respectively, 
in  diameter,  and  the  forms  were  constructed  similarly  to  the 
forms  shown  in  Fig.  77,  except  that  at  the  bottom  the  lower 


186 


REINFORCED  CONCRETE 


side  ribs  were  connected  to  the  bottom  rib  by  a  horizontal  joint, 
and  the  spacing  of  the  ribs  was  2  feet  6  inches,  center  to  center. 
Fig.  78  shows  the  form  for  the  7-foot  6-inch  conduit.  The  cen- 
tering for  the  9-foot  and  10-foot  conduits  was  constructed  sim- 
ilarly to  the  7-foot  6-inch  conduit,  except  that  the  ribs  were 
divided  into  7  parts  instead  of  5  parts  as  shown  in  Fig.  78.  The 
spacing  of  the  braces  depended  on  the  thickness  of  the  lagging. 
For  lagging  1  inch  by  2J  inches,  the  braces  were  spaced  18 
inches,  center  to  center ;  and  for  2-  by  3-inch  lagging,  the  spac- 
ing of  the  bracing  was  2  feet  6  inches. 

These  forms  were  constructed  in  lengths  of  8  feet.    The  lag- 
3>/  ging  for  the  smaller  sizes 

^  PPC  of  the  conduits  was  1  inch 
by  2f  inches,  and  for  the 
larger  sizes  2  by  3  inches ; 
all  of  this  was  made  of 
dressed  lumber  and  cov- 
ered with  No.  27  galvan- 
ized sheet  iron.  The  brac- 
ing of  the  forms  was 
arranged  to  permit  the 
centering  to  be  taken 
apart  and  brought  for- 
ward through  the  sections 
in  front.  Three  sets  of 
these  forms  were  required 
for  each  conduit.  The 
specifications  required  that  the  centering  be  left  in  place  for 
at  least  60  hours  after  the  concrete  had  been  placed.  It  was 
also  required  that  this  work  should  be  monolithic— that  is,  the 
contractor  could  build  as  long  a  section  as  he  could  finish  in  a 
day,  and  that  the  sections  should  be  securely  keyed  together. 
Forms  for  Walls.  The  forms  for  concrete  walls  should  be 
built  strong  enough  to  insure  their  retaining  their  correct  posi- 
tion while  the  concrete  is  being  placed  and  rammed.  In  high, 
thin  walls,  a  great  deal  of  care  is  required  to  keep  the  forms  in 
place  so  that  the  wall  will  be  true  and  straight. 


Fig.  78.   Form  for  Construction  of 
Horseshoe-Shaped  Conduit 


REINFORCED  CONCRETE 


187 


Fig.  79  shows  a  very  common  method  of  constructing  these 
forms.  The  plank  against  which  the  concrete  is  placed  is  sel- 
dom less  than  1J  inches  thick,  and  is  usually  2  inches  thick.  One- 
inch  plank  is  sometimes  used  for  very  thin  walls,  but  the  sup- 
ports must  be  placed  close.  The  planks  are  generally  surfaced 
on  the  side  against  which  the  concrete 
is  placed.  The  vertical  timbers  that 
hold  the  planks  in  place  will  vary  in 
size  from  2  by  4  inches  to  4  by  6 
inches,  or  will  be  even  larger,  depend- 
ing on  the  thickness  of  the  wall,  the 
spacing  of  these  vertical  timbers,  etc. 
The  vertical  timbers  are  always  placed 
in  pairs,  and  are  usually  held  in  place 
by  means  of  heavy  wires. 

Forms  for  Centers  of  Arches 

General  Specifications.  The  cen- 
ters for  stone,  plain  concrete,  and  re- 
inforced concrete  arches  are  similar 
in  construction.  A  reinforced  con- 
crete arch  of  the  same  span  and 
designed  for  the  same  loading  will  not 
be  so  heavy  as  a  plain  concrete  or 
stone  arch,  and  the  centers  need  not 
be  constructed  so  strong  as  for  the 
other  types  of  arches.  One  essential 
difference  in  the  centering  for  stone 
arches  and  that  for  concrete  or  rein- 
forced concrete  arches  is  that  center- 
ing for  the  latter  types  serves  as  a  mold  for  shaping  the  soffit  of 
the  arch  ring,  the  face  of  the  arch  ring,  and  the  spandrel,  walls. 

The  successful  construction  of  arches  depends  nearly  as  much 
on  the  centers  and  their  supports  as  it  does  on  the  design  of  the 
arch.  The  centers  should  be  as  well  constructed  and  the  sup- 
ports as  unyielding  as  it  is  possible  to  make  them.  When  it  is 
necessary  to  use  piles,  they  should  be  as  well  driven  as  perma- 


ma® 


Fig.  79..    Typical  Wall 
Form 


188 


REINFORCED  CONCRETE 


nent  foundation  piles,  and  the  load,  in  most  cases,  should  not 
be  heavier  than  that  on  permanent  piles. 

Classes  of  Centers.  There  are  two  general  classes  of  cen- 
ters—those which  act  as  a  truss,  and  those  in  which  the  support, 
at  the  intersection  of  braces,  rests  on  a  pile  or  footing.  Trusses 
are  used  when  it  is  necessary  to  span  a  stream  or  roadway. 
Sometimes  the  length  of  the  span  for  the  centering  is  very 
short,  or  there  is  a  series  of  short  spans,  or  the  span  may  be 
equal  to  that  of  the  arch.  The  trusses  must  be  carefully  de- 
signed, in  order  that  the  deflection  and  deformation  due  to  the 
changes  in  the  loading  will  be  reduced  to  a  minimum.  By  plac- 
ing a  temporary  load  on  the  cen- 
ters at  the  crown,  the  deforma- 
tion during  construction  may  be 
very  greatly  reduced.  This  load 
is  removed  as  the  weight  of  the 
arches  comes  on  the  centers. 
(For  the  design  of  trusses,  the 
reader  is  referred  to  the  Instruc- 
tion Papers,  or  other  treatises,  on 
Bridge  Engineering  and  on  Roof 
Trusses.) 

The  lagging  for  concrete  arches 
usually  consists  of  2-  by  3-inch 
or  2-  by  4-inch  plank,  either  set 
on  edge  or  laid  flat,  depending 
on  the  thickness  of  the  arch  and 

the  spacing  of  the  supports.  The  side  on  which  the  concrete 
is  laid  is  generally  surfaced.  The  lagging  is  often  supported  on 
ribs  constructed  of  2-  by  12-inch  plank,  on  the  back  of  which  is 
placed  a  2-inch  plank  cut  to  a  curve  parallel  with  the  intrados. 
These  2-  by  12-inch  planks  are  set  on  the  timber  used  to  cap 
the  piles,  and  are  usually  spaced  about  2  feet  apart.  All  the 
supports  should  be  well  braced.  The  centers  should  be  con- 
structed to  give  a  camber  to  the  arch  about  equal  to  the  deflec- 
tion of  the  arch  when  under  full  load.  It  is,  therefore, 
necessary  to  make  an  allowance  for  the  settlement  of  centering, 


Fig.  80.  Wedges  Used  in  Placing 
and  Removing  Forms 


REINFORCED  CONCRETE 


189 


for  the  deflection  of  the  arch  after  the  removal  of  the  centering, 
and  for  permanent  camber. 

The  centers  should  be  constructed  so  that  they  can  easily  be 
taken  down.  To  facilitate  the  striking  of  centers,  the  practice 
is  to  support  them  on  folding  wedges  or  sand  boxes.  When  the 
latter  method  is  used,  the  sand  should  be  iine,  clean,  and  per- 
fectly dry,  and  the  boxes  should  be  sealed  around  the  plunger 
with  cement  mortar.  Striking  forms  by  means  of  wedges  is 
the  commoner  method.  The  type  of  wedge  generally  used  is 


Fig.  81.  Typical  Arch  Form  Used  at  175th  Street,  New  York  City 

shown  in  Fig.  80-a,  although  sometimes  three  wedges  are  -used, 
as  sirown  by  Fig.  80-6.  They  are  from  1  foot  to  2  feet  long,  6 
to  8  inches  wide,  and  have  a  slope  of  from  1 :  6  to  1 : 10.  The 
centering  is  lowered  by  driving  back  the  wedges ;  and  to  do  this 
slowly,  it  is  necessary  that  the  wedges  have  a  very  slight  taper. 
All  wedges  should  be  driven  equally  when  the  centering  is  being 
lowered.  The  wedges  should  be  made  of  hardwood,  and  are 
placed  on  top  of  the  vertical  supports  or  on  timbers  which  rest 
on  the  supports.  They  should  be  placed  at  about  the  same 
elevation  as  the  springing  line  of  the  arch. 

Forms  for  Arch  at  175th  Street,  New  York  City.    In  build- 
ing the  175th  Street  Arch  in  New  York  City,  the  forms  were 


190  REINFORCED  CONCRETE 

so  built  that  they  could  be  easily  moved.  The  arch  is  elliptical 
and  is  built  of  hard-burned  brick  and  faced  with  granite.  The 
span  of  the  arch  is  66  feet;  the  rise  is  20  feet;  the  thickness 
of  the  arch  ring  is  40  inches  and  48  inches,  at  the  crown  and 
the  springing  line,  respectively;  and  the  arch  is  built  on  a 
9-degree  skew.  The  total  length  is  800  feet. 

The  arch  is  constructed  in  sections,  the  centering  being  sup- 
ported on  11  trusses  placed  perpendicular  to  the  axis  of  the 
arch  and  having  the  form  and  dimensions  shown  in  Fig.  81. 
The  trusses  are  placed  5  feet  on  centers,  and  are  supported  at 
the  ends  and  middle  by  three  lines  of  12-  by  12-inch  yellow-pine 
caps.  The  caps  are  supported  by  12-  by  12-inch  posts,  spaced 
5  feet  center  to  center,  and  rest  on  timber  sills  on  concrete 
foundations.  The  upper  and  lower  chord  members  of  the  trusses 
are  of  long-leaf  yellow  pine,  but  the  diagonals  and  verticals  are 
of  short-leaf  yellow  pine.  The  lagging  is  2f  -  by  6-inch  long-leaf 
yellow-pine  plank.  The  connections  of  the  timbers  are  made 
by  means  of  f-inch  steel  plates  and  I -inch  bolts,  arranged  as 
shown  in  the  illustration.  As  it  was  absolutely  necessary  to 
have  the  forms  alike,  so  that  they  could  be  moved  along  the 
arch  and  would  at  all  times  fit  the  brickwork,  they  were  built  on 
the  ground  from  the  same  pattern,  and  hoisted  to  their  places 
by  two  guyed  derricks  with  70-foot  booms. 

On  the  12-  by  12-inch  cap  was  a  3-  by  8-inch  timber,  on  which 
the  double  wedges  were  placed.  When  it  was  necessary  to  move 
the  forms,  the  wedges  were  removed,  the  forms  rested  on  the 
rollers,  and  there  was  then  a  clearance  of  about  21  inches  between 
the  brickwork  and  the  lagging.  The  timber  on  which  the  rollers 
ran  was  faced  with  a  steel  plate  £  inch  by  4  inches  in  dimensions. 
The  forms  were  moved  forward  by  means  of  the  derricks.  The 
settlement  of  the  forms  under  the  first  section  constructed  was 
i  inch ;  and  the  settlement  of  the  arch  ring  of  that  section,  after 
the  removal  of  forms,  was  £  inch.* 

Forms  for  Bridge  at  Canal  Dover,  Ohio.f  The  details  of 
the  centering  used  in  erecting  one  of  the  spans  of  a  reinforced 


*  Engineering  Record,  October  5,  1907. 
t  /W'd.,  February  9,  1907. 


REINFORCED  CONCRETE 


191 


concrete  bridge  over 
the  Tuscarawas  River 
at  Canal  Dover,  Ohio, 
are  shown  in  Figs.  82 
and  83.  This  span  was 
106  feet  and  8  inches 
long;  there  were  two 
other  spans  of  the 
same  length  in  the 
bridge,  and  a  canal 
span  of  70  feet.  The 
centering  for  the  canal 
span  was  built  in  6 
bents,  each  bent  having 
7  piles.  A  clear  water- 
way of  18  feet  was 
required  in  the  canal 
span  by  the  state  canal 
commissioner,  and  this 
passage  was  arranged 
under  the  center  of  the 
arch.  The  piles  were 
driven  by  means  of  a 
scow.  The  cap  for  the 
piles  was  a  3-  by  12- 
inch  timber.  Planks  2 
inches  thick  were  sawed 
to  the  correct  curva- 
ture, and  nailed  to  the 
2-  by  12-inch  joists, 
which  were  spaced 
about  12  inches  apart. 
The  lagging  was  1  inch 
thick,  and  was  nailed 
to  the  curved  plank. 
The  wedges  were  made 
and  used  as  shown. 


192 


REINFORCED  CONCRETE 


The  centering  was  constantly  checked;  this  was  found  impor- 
tant after  a  strong  wind.  The  centering  for  the  other  two  of 
the  main  arches  was  constructed  as  in  the  arch  shown. 

After  some  difficulty  had  been  experienced  in  keeping  the 
forms  in  place  during  the  concreting  of  the  first  arch,  the  con- 


Fig.  83.  Centers  for  Bridge  at  Canal  Dover,  Ohio 

crete  for  the  other  arches  was  placed  in  the  order  shown  in  Fig. 
84,  and  no  other  difficulty  was  encountered.  Sections  1  and  1 
were  first  placed,  then  2  and  2,  etc.,  section  6  being  the  last. 

The  concreting  on  the  canal  span  was  begun  in  the  late  fall, 
and  finished  in  12  days;  the  forms  were  lowered  by  means  of 
the  wedges  five  weeks  later.  The  deflection  at  the  crown  was  0.5 


Fig.  84.     Diagram  showing  Order  of  Placing 
Concrete  in  Bridge  at  Canal  Dover 

inch,  and  after  the  spandrel  walls  were  built  and  the  fill  made, 
there  was  an  additional  deflection  of  0.4  inch.  In  building  the 
forms,  an  allowance  of  -^J.^  part  of  the  span  was  made,  to  allow 
for  this  deflection.  The  deflections  at  the  crown  of  the  other 
three  arches  were  0.6  inch,  1.45  inches,  and  1.34  inches. 


REINFORCED  CONCRETE  193 

FINISHING  SURFACES  OF  CONCRETE 

Imperfections.  To  give  a  satisfactory  finish  to  exposed 
surfaces  of  concrete  is  a  rather  difficult  problem.  In  many  in- 
stances, when  the  forms  are  taken  down,  the  surface  shows  the 
joints,  knots,  and  grain  of  the  wood;  it  has  more  the  appearance 
of  a  piece  of  rough  carpentry  work  than  of  finished  masonry. 
Moreover,  failure  to  tamp  or  flat-spade  the 'surf  aces  next  to  the 
forms  will  result  in  rough  places  or  stone  pockets.  Lack  of 
homogeneity  in  the  concrete  will  cause  a  variation  in  the  surface 
texture.  Diversity  of  color,  or  discoloration,  is  one  of  the  most 
common  imperfections.  Old  concrete  adhering  to  the  forms  will 


Fig.  85.   Sheet-Iron  Plate  for  Giving  Finish  Surface  to  Concrete 

leave  pits  in  the  surface,  and  the  pulling-off  of  the  concrete  in 
spots,  as  a  result  of  its  adhering  to  the  forms  when  they  are 
removed,  will  cause  a  roughness. 

To  guard  against  these  imperfections,  the  forms  must  be  well 
constructed  of  dressed  lumber,  and  the  pores  should  be  care- 
fully filled  with  soap  or  paraffin.  The  concrete  should  be  thor- 
oughly mixed,  and,  when  placed,  care  should  be  taken  to  compact 
it  thoroughly,  next  to  the  forms.  Differences  in  color  are  usually 
due  to  the  leaching-out  of  lime,  which  is  deposited  in  the  form 
of  an  efflorescence  on  the  surface;  or  to  the  use  of  different 
cements  in  adjacent  parts  of  the  same  work.  Variation  due 
to  the  latter  cause  can  almost  always  be  avoided  by  using  the 
same  brand  of  cement  on  the  entire  work.  (The  matter  of 
efflorescence  is  treated  later.) 


194 


REINFORCED  CONCRETE 


86.     Diagram    Showing    Method    of 
iving  Masonry  Facing  to  Concrete 


Plastering.     Plastering  is  not  usually  satisfactory,  although 

there  are  cases  where  a  mixture  of  equal  parts  of  cement  and 

sand  has,  apparently,  been  successful,  and,  when  finished  rough, 

it  did  not  show  any  cracks.    It  is  generally  considered  impossible 

w////////////////////y//////////^  to  apply  mortar  in  thin 

layers  to  a  concrete  sur- 
face, and  make  it  adhere 
for  any  length  of  time. 
When  the  plastering  be- 
gins to  scale  off,  the  con- 
crete looks  worse  than 
with  an  unfinished  sur- 
face. This  paragraph  is 
intended  more  as  a  warn- 
ing against  this  manner  of  finishing  concrete  surfaces  than  as 
a  description  of  it  as  an  approved  method  of  finish. 

Mortar  Facing.  A  method  of  placing  mortar  facing  that 
has  been  found  very  satisfactory,  and  has  been  adopted  exten- 
sively in  the  last  few  years,  is  as  follows:  A  sheet-iron  plate, 
6  or  S  inches  wide  and  about  5  or  6  feet  long,  has  riveted  across 
it  on  one  side,  every  two 
feet  or  so,  angles  of 
f-inch  size,  or  of  such 
other  size  as  may  be  nec- 
essary to  give  the  desired 
thickness  of  mortar  fac- 
ing, Fig.  85.  In  opera- 
tion, the  ribs  of  the  angles 
are  placed  against  the 
forms,  and  the  space  be-  Fig"  87'  Typical  Facing  1Iammer 
tween  the  plate  and  forms  is  filled  with  mortar,  mixed  in  small 
batches  and  thoroughly  tamped.  The  concrete  back  filling  is 
then  placed,  the  mold  is  withdrawn,  and  the  facing  and  back 
filling  are  rammed  together.  The  mortar  facing  is  mixed  in 
the  proportion  of  1  part  cement,  to  1,  2,  or  3  parts  sand; 
usually  a  1 : 3  mixture  is  employed,  mixed  wet  and  in  small 
batches  as  it  is  needed.  As  mortar  facing  shows  the  roughness 


REINFORCED  CONCRETE 


195 


of  the  forms  more  readily  than  concrete  does,  care  is  required, 
in  constructing,  to  secure  a  smooth  finish.    When  the  forms  are 


Fig.  88.     Power-Driven   Hand  Tool  for 

Surfacing  Concrete 
Courtesy  of  "Scientific  American" 

removed,  the  face  may  be  treated  either  by  washing  or  by  tool 
dressing  as  described  in  the  succeeding  paragraphs. 

Masonry   Facing.     Concrete   surfaces  may   be   finished  to 
represent   ashlar  masonry.     The   process   is  similar  to   stone 


196 


REINFORCED  CONCRETE 


dressing,  and  any  of  the  forms  of  finish  employed  for  cut  stone 
can  be  used  for  concrete.  Very  often,  when  the  surface  is 
finished  to  represent  ashlar  masonry,  vertical  and  horizontal 
three-sided  pieces  of 'wood  are  fastened  to  the  forms  to  make 
V-shaped  depressions  in  the  concrete,  as  shown  in  Fig.  86. 

Hammer  Dressing.  In  constructing  the  Harvard  Univer- 
sity stadium,  care  was  taken,  after  the  concrete  was  placed  in 
the  forms,  to  force  the  stones  back  from  the  face  and  permit 
the  mortar  to  cover  every  stone.  When  the  forms  were  re- 
moved, the  surface  was  picked  with  the  tool  shown  in  Fig.  87. 
A  pneumatic  tool  has  also  been  devised  for  this  purpose. 


(a) 


Fig.  89.     Quimby's  Finish  on  Concrete  Surfaces,      (a)    Aggregate 
TVlnch  White  Pebbles  ;  (b)  Aggregate  |-Inch  Screened  Stone 

The  number  of  square  feet  to  be  picked  per  day  depends  on 
the  hardness  of  the  concrete.  If  the  picking  is  performed  by 
hand,  it  is  done  by  a  common  laborer,  and  he  is  expected  to 
average  50  square  feet  per  day  of  10  hours.  With  a  pneumatic 
tool,  a  man  would  cover  from  400  to  500  square  feet  a  day. 

Recently  a  motor-driven  hand  tool,  Fig.  88,  has  been  in- 
vented.  It  is  driven  through  a  flexible  shaft  by  a  motor 
carried  by  the  operator.  Its  weight,  including  the  weight  of 
the  motor,  is  only  about  20  pounds.  The  motor  may  take  its 
actuating  current  from  an  ordinary  light  socket.  The  concrete 
is  cut  by  the  teeth  of  a  number  of  wheels  revolving  at  high 
speed.  This  machine  will  dress  700  to  900  square  feet  a  day. 


REINFORCED  CONCRETE  197 

Granolithic  Finish.  Several  concrete  bridges  in  Philadel- 
phia have  been  finished  according  to  the  following  specifications 
and  their  appearance  is  very  satisfactory: 

Granolithic  surfacing,  where  required,  shall  be  composed  of  1  part 
cement,  2  parts  coarse  sand  or  gravel,  and  2  parts  granolithic  grit,  made 
into  a  stiff  mortar.  Granolithic  grit  shall  be  granite  or  trap  rock, 
crushed  to  pass  a  |-inch  sieve,  and  screened  of  dust.  For  vertical  sur- 
faces, the  mixture  shall  be  deposited  against  the  face  forms  to  a  mini- 
mum thickness  of  1  inch,  by  skilled  workmen,  as  the  placing  of  the 
concrete  proceeds  ;  and  it  thus  forms  a  part  of  the  body  of  the  work. 
Care  must  be  taken  to  prevent  the  occurrence  of  air  space  or  voids  in 
the  surface.  The  face  shall  be  removed  as  soon  as  the  concrete  has 
sufficiently  hardened ;  and  any  voids  that  may  appear  shall  be  filled 
with  the  mixture.  The  surface  shall  then  be  immediately  washed  with 
water  until  the  grit  is  exposed  and  rinsed  clean,  and  shall  be  protected 
from  the  sun  and  kept  moist  for  three  days.  For  bridge-seat  courses 
and  other  horizontal  surfaces,  the  granolithic  mixture  shall  be  deposited 
on  the  concrete  to  a  thickness  of  at  least  1|  inches,  immediately  after 
the  concrete  has  been  tamped  and  before  it  has  set,  and  shall  be 
troweled  to  an  even  surface,  and,  after  it  has  set  sufficiently  hard,  shall 

be  washed  until  the  grit  is  exposed. 

\ 

The  success  of  this  method  depends  greatly  on  the  removal  of 
the  forms  at  the  proper  time.  In  general,  the  washing  is  done 
the  day  following  that  on  which  the  concrete  is  deposited.  The 
fresh  concrete  is  scrubbed  with  an  ordinary  scrubbing  brush, 
removing  the  film  and  the  impressions  of  the  forms,  and  expos- 
ing the  sand  and  stone  of  the  concrete.  If  this  is  done  when 
the  material  is  at  the  proper  degree  of  hardness,  a  few  rubs  of 
an  ordinary  house  scrubbing  brush,  with  a  free  flow  of  water 
to  cut  and  to  rinse  clean,  are  all  the  work  required.  The  cost 
of  scrubbing  is  small  if  done  at  the  right  time.  A  laborer  will 
wash  100  square  feet  in  an  hour ;  but  if  that  same  area  is  per- 
mitted to  get  hard,  it  may  require  two  men  a  day,  with  wire 
brushes,  to  secure  the  desired  results.  The  practicability  of 
removing  the  forms  at  the  proper  time  for  sucfi  treatment 
depends  upon  the  character  of  the  structure  and  the  conditions 
under  which  the  work  must  be  done.  This  method  is  applicable 
to  vertical  walls,  but  it  would  not  be  applicable  to  the  soffit  of 
an  arch,  Tig.  89. 

The  Acid  Treatment.  This  process,  which  has  been  very 
successfully  used,  consists  in  washing  the  surface  of  the  con- 


198  REINFORCED  CONCRETE 

crete  with  diluted  acid,  then  with  an  alkaline  solution.  The 
diluted  acid  is  applied  first,  to  remove  the  cement  and  expose 
the  sand  and  stone;  the  alkaline  solution  is  then  applied  to 
remove  all  of  the  free  acid ;  and,  finally,  the  surface  is  washed 
with  clear  water.  The  treatment  may 
be  applied  at  any  time  after  the  forms 
are  removed;  it  is  simple  and  effective. 
Limestone  cannot  be  used  in  the  con- 
crete for  any  surfaces  that  are  to  have 
this  treatment,  as  the  limestone  would 
be  affected  by  the  acid. 

Dry  Mortar  Finish.  The  dry  mor- 
tar method  consists  in  using-  a  dry,  rich 
mixture  with  finely  crushed  stone.  The 
concrete  is  usually  composed  of  1  part 
cement,  3  parts  sand,  and  3  parts 
crushed  stone  known  as  the  £-inch  size, 
mixed  dry  so  that  no  mortar  will  flush 
to  the  surface  when  well  rammed  in 
the  forms.  The  concrete,  when  placed, 
is  not  spaded  next  to  the  forms  and, 
since  it  is  dry,  there  is  no  smooth  mor- 
tar surface,  but  there  should  be  an  even- 
grained,  rough  surface.  With  the  dry 
mixture,  the  imprint  of  the  joints  of 
the  forms  is  hardly  noticed,  and  the 
grain  of  the  wood  is  not  seen  at  all. 

Fig.  90.  Typical  Molded     This  style  of  finish  has  been  extensively 
Concrete  Baluster  j  •     j.i_     o      ,v  T»     i  n  ™  • 

used  in  the  South  Park  system  of  Chi- 
cago, and  there  has  been  no  efflorescence  apparent  on  the  surface, 
which  is  explained  by  "the  dryness  of  the  mix  and  the  porosity 
of  the  surface". 

Cast-Slab  Veneer.  Cast-concrete-slab  veneer  can  be  made 
of  any  desired  thickness  or  size.  It  is  set  in  place  like  stone 
veneer,  with  the  remainder  of  the  concrete  forming  the  backing. 
It  is  usually  cast  in  wood  molds,  face  down.  A  layer  of  mortar, 
1  part  cement,  1  part  sand,  and  2  or  3  parts  fine  stone  or  coarse 


REINFORCED  CONCRETE  199 

sand,  is  placed  in  the  mold  to  a  depth  of  about  1  inch,  and' then 
the  mold  is  filled  up  with  a  1:2:4  concrete.  Any  steel  rein- 
forcement that  is  desired  may  be  placed  in  the  concrete.  Usually, 
cast-concrete-slab  veneer  is  cheaper  than  concrete  facing  cast 
in  place,  and  gives  a  better  surface'finish. 

Moldings  and  Ornamental  Shapes.  Concrete  is  now  in 
demand  in  ornamental  shapes  for  buildings  and  bridges.  The 
shapes  may  be  either  constructed  in  place,  or  molded  in  sections 
and  placed  the  same  as  cut  stone.  Plain  cornices  or  panels  are 
usually  constructed  in  place,  but  complicated  molding  or  balus- 
ters, Fig.  90,  are  frequently  made  in  sections  and  erected  in 
separate  pieces. 

Colors  for  Concrete  Finish.  Coloring  matter  has  not  been 
used  very  extensively  with  concrete,  except  in  ornamental  work. 
It  has  not  been  very  definitely  determined  what  coloring  matters 
are  detrimental  to  concrete.  Lampblack  (boneblack)  has  been 
used  more  than  any  other  coloring  matter.  It  gives  different 
shades  of  gray,  depending  on  the  amount  used.  Common  lamp- 
black and  Venetian  red  should  not  be  used,  as  they  are  likely 
to  run  or  fade.  Dry  mineral  colors,  mixed  in  proportions  of 
2  to  10  per  cent  of  the  cement,  give  satisfactory  results.  Red 
lead  should  never  be  used ;  even  1  per  cent  is  injurious  to  the 
concrete.  Variations  in  the  color  of  cement  and  in  the  character 
of  the  sand  .used  will  affect  the  results  obtained  in  using  coloring 
matter. 

Painting  Concrete  Surfaces.  Special  paints  are  made  for 
painting  concrete  surfaces,  since  ordinary  paints,  as  a  rule,  are 
not  satisfactory.  Before  the  paint  is  applied,  the  surface  of  the 
wall  should  be  washed  with  dilute  sulphuric  acid,  1  part  acid  to 
100  parts  water. 

Finish  for  Floors.  Floors  in  manufacturing  buildings  are 
often  finished  with  a  1-inch  coat  of  cement  and  sand,  mixed  in 
the  proportions  of  1  part  cement  to  1  part  sand ;  or  1  part  cement 
to  2  parts  sand.  This  finishing  coat  must  be  put  on  before  the 
concrete  base  sets,  or  it  will  break  up  and  shell  off,  unless  made 
very  thick— from  1£  to  2  inches.  A  more  satisfactory  method  of 
finishing  such  floors  is  to  put  2  inches  of  cinder  concrete  on  the 


200  REINFORCED  CONCRETE 

concrete  base,  and  then  put  the  finishing  coat  on  the  cinder 
concrete.  The  finish  coat  and  cinder  concrete  bond  together, 
making  a  thickness  of  3  inches.  The  cinder  concrete  may  con- 
sist of  a  mixture  of  1  part  cement,  2  parts  sand,  and  6  parts 
cinders,  and  may  be  put  down  at  any  time— that  is,  this  method 
of  finishing  a  floor  can  be  used  as  satisfactorily  on  an  old  con- 
crete floor  as  on  one  just  constructed. 

In  office  buildings,  and  generally  in  factory  buildings,  a  wood 
floor  is  laid  over  the  concrete.  Wood  stringers  are  first  laid  on 
the  concrete,  about  1  foot  or  1£  feet  apart.  The  stringers  are  2 
inches  thick  and  3  inches  wide  on  top,  with  sloping  edges.  The 
space  between  the  stringers  is  filled  with  cinder  concrete,  as 
shown  in  Fig.  91 ;  as  a  rule  this  is  mixed  1:3:6.  When  the 
concrete  has  set  the  flooring  is  nailed  to  the  stringers. 


Fig.  91.   Diagram  Showing  Typical  Cinder  Fill  between  Stringers 

Efflorescence.  The  white  deposit  found  on  the  surface  of 
concrete,  brick,  and  stone  masonry  is  called  efflorescence.  It  is 
caused  by  the  leaching  of  certain  lime  compounds,  which  are 
deposited  on  the  surface  by  the  evaporation  of  the  water,  and 
this  is  due,  primarily,  it  is  believed,  to  the  variation  in  the 
amount  of  water  used  in  mixing  the  mortar.  An  excess  of 
water  will  cause  a  segregation  of  the  coarse  and  fine  materials, 
resulting  in  a  difference  of  color.  In  a  very  wet  mixture  more 
lime  is  set  free  from  the  cement  and  brought  to  the  surface. 
If  great  attention  is  given  to  the  amount  of  water,  and  care  is 
taken  to  prevent  the  separation  of  the  stone  from  the  mortar 
when  deposited,  the  concrete  will  present  a  fairly  uniform  color 
when  the  forms  are  removed.  The  greater  danger  of  the 
efflorescence  at  joints  than  at  any  other  point  demands  special 
caution.  If  the  work  is  to  be  continued  within  24  hours,  and 
care  is  taken  to  scrape  and  remove  the  laitance,  and  then  if 
before  the  next  layer  is  deposited,  the  scraped  surface  is  coated 


REINFORCED  CONCRETE 


201 


with  a  thin  cement  mortar,  the  joint  should  be  impervious  to 
moisture,  and  no  trouble  with  efflorescence  should  be  experienced. 

A  very  successful  method  of  removing  efflorescence  from  a 
concrete  surface  consists  in  applying  a  wash  of  dilute  hydro- 
chloric acid.  The  wash  consists  of  1  part  acid  to  5  parts 
water,  and  is  applied  with  scrubbing  brushes.  Water  is  kept 
constantly  playing  on  the  work,  by  means  of  a  hose,  to  prevent 
the  penetration  of  the  acid.  The  cleaning  is  very  satisfactory, 
and  for  plain  surfaces  costs  about  20  cents  per  square  yard. 

Laitance.  Laitance  is  whitish,  spongy  material  that  is 
washed  out  of  the  concrete  when  it  is  deposited  in  water.  Before 
settling  on  the  concrete,  it  gives  the  water  a  milky  appearance. 
It  is  a  semifluid  mass,  composed  of  a  very  fine,  flocculent  matter 
in  the  cement ;  it  generally  contains  hydrare  of  lime,  stays  in  a 
semifluid  state  for  a  long  time,  and  acquires  very  little  hardness 
at  its  best.  Laitance  interferes  with  the  bonding  of  the  layers 
of  concrete,  and  should  always  be  thoroughly  cleaned  from  the 
surface  before  another  layer  of  concrete  is  placed. 

BENDING  OR  TRUSSING  BARS 

Bending  Details.  Drawings  showing  all  the  bending  details 
of  the  bars  for  all  reinforced  concrete  work  should  be  made 
before  the  steel  is  ordered.  The  designing  engineer  should  detail 
a  few  of  the  typical  beams  and  girders  to  show,  in  a  general  way, 
what  length  of  bars  will  be  required,  the  number  of  turned-up 


-*  -i-v 

SECTION  f}ff 

Fig.  92.   Details  of  Beam  Construction 

bars,  the  number,  size,  and  spacing  of  stirrups,  and  the  dimen- 
sions of  the  concrete.  This  information  will  be  a  guide  for  the 
construction  engineer  in  making  up  the  details  required  properly 
to  construct  the  work.  Fig.  92  shows  the  manner  in  which  the 


202 


REINFORCED  CONCRETE 


designing  engineer  should  detail  a  typical  beam  so  that  the  con- 
structing engineer  can  develop  these  details 


shown  in  Fig.  93. 


/tfk. 

N?of 
Be&ms 

/V?of  Bars 
in  each  Beam 

Shape 

Slirrups 

BS 

64 

*-'*'.'. 
16  -O' 

Straight 

fa 
t*i 

"^ 

.4 

*''*'*    „ 
SO'-  8" 

-^Q,                           ,^4^ 
^s?*         ff-o"          2x^  /V5" 

^-*'-o* 

Fig.  93.   Bending  Details  for  Beams 

Tables  for  Bending  Bars.  A  simple  outfit  for  bending  the 
bars  cold  consists  of  a  strong  table,  the  top  of  which  is  con- 
structed as  shown  in  Fig.  94.  The  outline  to  which  the  bar  is  to 
be  bent  is  laid  out  on^the  table,  and  holes  are  bored  at  the  points 
where  the  bends  are  to  be  made.  Steel  plugs  5  to  6  inches  long 
are  then  placed  in  these  holes.  Short  pieces  of  boards  are  nailed 
to  the  table  where  necessary,  to  hold  the  bar  in  place  while  being 


a 

i     i 

1    1"  )(  6"  Plank 

5 

"—  [I       s~c 

-<  
i 

•  •• 

H 

i    |£\^X^" 

\    2"  Plank        ^^J 

! 

^7 

|    | 

J 

! 

Fig.  94.   Plan  of  Bending  Table 

bent.  The  bar  is  then  placed  in  the  position  A-B,  Fig.  94,  and 
bent  around  the  plugs  C  and  D,  and  then  around  the  plugs  E  and 
F,  until  the  ends  E  H  and  F  G  are  parallel  to  A  B.  When  bends 
with  short  radii  are  required,  the  bars  are  placed  in  the  vise, 
near  the  point  where  the  bend  is  to  be  made,  and  the  end  of  the 


Fig.  95.   Type  of  Lever  Bender 

bar  is  pulled  around  until  the  required  angle  is  secured.  The 
vise  is  usually  fastened  to  the  table.  The  lever  shown  in  Fig.  95 
is  also  used  in  making  bends  of  short  radii.  This  is  done  by 
placing  the  bar  between  the  prongs  of  the  lever  and  pulling 


REINFORCED  CONCRETE 


203 


the  end  of  the  lever  around  until  the  required  shape  of  the  bar 
is  obtained. 

Bars  with  Hooked  Ends.  When  plain  bars  are  used  for 
reinforced  concrete,  architects  and  engineers  very  often  require 
that  the  ends  of  all  the  bars  in  the  beams  and  girders  shall  be 


Fig.  96.   Bars  with  Hooked  Ends 

hooked,  as  shown  in  Fig.  96.  This  is  done  to  prevent  the  bars 
from  slipping  before  their  tensile  strength  is  fully  developed. 
Slab  Bars.  To  secure  the  advantage  of  a  continuous  slab, 
it  is  very  often  required  that  a  percentage  of  the  slab  bars,  usu- 
ally one-half,  shall  be 
turned  up  over  each 
beam.  Construction 
companies  have  different 
methods  of  bending  and 
holding  these  bars  in  Fig' 97'  slabBars 

place;  but  the  method  shown  in  Fig.  97  will  insure  good 
results,  as  the  slab  bars  are  well  supported  by  the  two  longitu- 
dinal bars  which  are  wired  to  the  tops  of  the  stirrups.  Fig.  98 
shows  the  bending  details  of  slab  bars,  the  beams  being  spaced 


k  /5  V  /4  '-41 —  2L/0^-^  14  \l(re-/4  *H —  2-/o"  H'  /^V 

=^  L^l^^l  l^^ji^L^I  |^J- 


<$-^ 


^-^? 


Fig.  98.   Diagram  Showing  Bent  Bars  for  Slabs 

six  feet,  center  to  center.    When  slabs  are  designed  as  simple 
beams  (Wl  +  8)  none  of  the  slab  bars  are  bent. 

Stirrups.  Fig.  99  shows  the  bending  of  the  bars  for  stir- 
rups. The  ends  of  the  stirrups  rest  on  the  forms  and  support 
the  beam  bars,  which  assist  in  keeping  these  bars  in  place.  The 
ends  of  the  stirrups  never  show  on  the  bottom  of  the  slab  of  the 
finished  floor,  although  the  cut  ends  of  the  stirrups  rest  directly 
on  the.  slab  forms.  Sufficient  mortar  seems  to  get  under  the 


204 


REINFORCED  CONCRETE 


ends  of  the  stirrups  to  cover  them.    The  type  of  stirrup  shown 
in  Fig.  99-a  is  much  more  extensively  used  than  that  in  Fig. 


/n 


\J 

id 


(a) 


[\ 


(t) 


Fig.  99.   Diagram  Showing  Bending  Bars 
for  Stirrup 

99-b.     The  latter  is  usually  employed  when  a  large  amount  of 
steel  is  required,  or  if  the  stirrups  are  made  of  very  small  bars. 

Column  Bands.  In  Fig.  100 
two  types  of  column  bands  are 
shown.  Fig.  100-a  shows  bands 
for  a  square  or  a  round  column ; 
and  Fig.  100-&,  bands  for  a  rec- 
tangular column.  The  bar  which 
forms  the  band  is  bent  close 
around  each  vertical  bar  in  the 
columns,  and  therefore  assists 
in  holding  them  in  place.  Two 
bands  of  the  same  size  and  shape  are  used  for  Column  b. 
Spacers.  Spacers  for  holding  the  bars  in  place  in  beams 
and  girders  have  been  successfully  used.  These  spacers,  Fig. 
101,  are  made  of  heavy  sheet  iron.  They  are  fastened  to  the 
stirrups  by  means  of  the  loops  in  the  spacers.  The  ends  of  the 


Fig.  100.    Column  Bands 


Fig.  101.  Typical  Spacer  for 
Reinforcing  Bars 


Fig.  102.    Spacer  for  Slab  Bars 


spacers  which  project  out  to  the  forms  of  the  sides  of  the 
beams  should  be  made  blunt  or  rounded.    This  will  prevent  the 


REINFORCED  CONCRETE 


205 


206 


REINFORCED  CONCRETE 


ends  of  the  spacers  from  being  driven  into  the  forms  when  the 
concrete  is  being  tamped.  The  number  of  spacers  required 
(usually  2  to  4)  will  depend  on  the  lengths  of  the  beams. 

Several  devices  have  been  manufactured  for  holding  slab  bars 
while  the  concrete  is  being  poured.  Fig.  102  shows  a  spacer 
made  by  the  Concrete  Steel  Company,  of  Philadelphia. 

Unit  Frames.  Companies  making  a  specialty  of  supplying 
reinforcing  steel  generally  have  their  own  methods  of  making 
the  bars  for  a  beam  into  a  unit.  This  is  accomplished  in  differ- 
ent ways.  The  frames  are  made  up  at  a  shop,  where  there  is 
machinery  for  doing  the  work,  and  shipped  to  the  job  as  a  unit. 
Fig.  103  shows  a  unit  made  by  the  Corrugated  Bar  Company. 

Fig.  104  shows  a  collapsible  frame  made  by  the  Concrete  Steel 
Company.  The  frame  is  made  up  of  four  small  bars,  usually 
%  inch  round,  and  the  stirrups  that  are  required  for  the  beam 
are  fastened  to  these  bars  by  clips  that  permit  the  frame  to  be 
folded  up  for  shipment.  When  the  frame  is  received  on  the  job 
it  is  unfolded,  placed  in  the  beam,  and  then  the  tension  bars  are 
put  in  the  frame  and  held  in  place  by  two  or  more  spacers. 

BONDING  OLD  AND  NEW  CONCRETE 

The  place  and  manner  of  making  breaks  or  joints  in  floor  con- 
struction at  the  end  of  a  day's  work  is  a  subject  that  has  been 

much  discussed  by  engineers  and 
construction  companies.  But 
there  has  not  yet  been  any  gen- 
eral agreement  as  to  the  best 
method  and  place  of  constructing 
these  joints.  Wherever  joints  are 
made,  great  care  should  be  exer- 
cised to  secure  a  bond  between  the 
new  and  the  old  concrete. 

Methods  of  Making  Bonds. 
(1)  Fig.  105  shows  a  sectional 
view  of  one  method  of  making  a  break  at  the  end  of  the  day's 
work;  this  method  has  been  used  extensively  and  successfully. 
The  stirrups  and  slab  bars  form  the  main  bond  between  the  old 


BONPINQ  BARS 

-4'-0"LONQ-^ 

_      • 

<   r-     *- 

/ 

f 

i 

X? 

JUINT^- 

r   i  • 

i  , 

Fig.   105.    Method  of  Bonding 

Old  and  New  Concrete 

in  Slab 


REINFORCED  CONCRETE 


207 


\ 


JOINT 


and  the  new  work,  if  the  break  is  left  more  than  a  few  hours; 
short  bars  in  the  top  of  the  slab  will  also  assist  in  making  a  good 
bond.  An  additional  number  of 
stirrups  should  be  used  where  the 
break  is  to  be  made  in  the  beam. 
Before  the  new  concrete  is  placed, 
the  old  concrete  should  be  well 
scraped,  thoroughly  soaked  with 
clean  water,  and  given  a  thin  coat 
of  neat  cement  grout.  An  objec- 
tion to  this  method  of  forming  a 
joint  is  that  shrinkage  may  cause  a  separation  of  the  concrete 
placed  at  the  two  different  times,  and  that  water  will  thus  find  a 
passage.  The  top  coat  that  is  generally  placed  later  greatly 
assists  in  overcoming  this  objection. 

(2)  Another  method  of  forming  stopping  places  is  by  divid- 
ing the  beam  vertically— that  is,  making  two  L-beams  instead  of 
one  T-beam,  Fig.  106.  Theoretically,  this  is  an  excellent  way, 


Fig.   106.    Method  of  Bonding 

Old  and  New  Concrete 

in  Beam 


nrfifs?          

~1      r~  ' 
'(VI 

-.    r  • 

1  (H 

ijiJi 

^JOINT 

'§ 

l! 

^-BONDING  BflR5 

,f, 

>L 

!«: 

BERW          

—  —  _  —  —   — 

—  i    <  — 

BflR 


Fig.  107.    Method  of  Bonding  Break  in 
Center  of  Span 

but  practically,  it  is  found  difficult  to  construct  the  forms  divid- 
ing  the  beam,  as  the  steel  is  greatly  in  the  way. 

(3)  The  method  of  stopping  the  work  at  the  center  of  the 
span  of  the  beams  and  parallel  to  the  girders  is  the  one  in  gen- 
eral use.  Fig.  107  illustrates  this  method.  Theoretically,  the 


208 


REINFORCED  CONCRETE 


slab  is  not  weakened;  and  as  the  maximum  bending  moment 
occurs  at  this  point,  the  shear  is  zero  and,  therefore,  the  beams 
are  riot  supposed  to  be  weakened,  except  for  the  loss  of  concrete 
in  tension,  and  this  is  not  considered  in  the  calculation.  The 
bottoms  of  the  beams  are  tied  together  by  the  steel  that  is  placed 
in  the  beams  to  take  the  tensile  stresses;  and  there  should  be 
some  short  bars  in  the  top  of  these  beams,  as  well  as  in  the  top 
of  the  slab,  to  tie  them  together.  The  objection  to  the  first 
method— that  any  shrinkage  at  the  joint  will  permit  water  to  pass 
through— is  greater  in  the  case  of  second  and  third  methods. 

DETAILS  OF  CONSTRUCTION 

Steel  Cores.  It  is  often  necessary  in  reinforced  concrete 
buildings  to  construct  columns  of  some  other  material  than  con- 
crete on  account  of  the 
large  space  that  would  be 
occupied  by  concrete  col- 
umns. In  such  cases  steel- 
core  columns  are  often 
used.  Fig.  108  shows  two 
types  of  the  steel  cores. 
Type  (a)  is  used  for 
round  columns  and  the 
steel  consists  of  four  angles,  but,  when  necessary,  plates  are 
inserted  between  the  angles  to  make  up  the  full  section.  Type 
(b)  is  used  for  square  columns.  In  determining  the  strength 


108 


Typical  Sections  of  Steel-Core 
Columns 


n 


i 


Fig.  109.  Tile  and  Joist  Construction 

of  these  columns,  the  Bureau  of  Building  Inspection  of  Phila- 
delphia permits  the  steel  to  be  figured  as  having  a  radius  of 
gyration  equal  to  that  of  the  concrete  section,  which  for  ordi- 


REINFORCED  CONCRETE 


209 


nary  story  heights  makes  the  permissible  loading  about  14,000 
pounds  per  square  inch,  but  additional  loading  is  not  permitted 
on  the  concrete.  The  steel  must  be  surrounded  by  at  least 
2  inches  of  concrete,  in  which  there  must  be  placed  4  small 
vertical  bars,  usually  f-inch,  banded  by  £-inch  bars,  12  inches 


Fig.  110.    Details  of  Spandrel 
Beams 


Fig,  111.    Details  of  Spandrel 
Beams 


on  centers.  The  loads  are  transmitted  from  the  beams  and 
girders  to  the  steel  by  means  of  large  steel  brackets  which  are 
riveted  to  the  columns.  The  work  is  riveted  up  in  the  usual 
manner  for  structural  steel. 

Tile  and  Joist  System.  The  tile  and  joist  system  of  con- 
structing fireproof  floors  is  found  economical  for  a  certain  class 
of  work.  It  is  probably  used  for  apartment  houses  of tener  than 


210  REINFORCED  CONCRETE 

anywhere  else.  The  advantage  of  this  construction  is  that  a  flat 
ceiling  is  secured.  The  structural  frame  of  the  building  may  be 
either  steel  or  reinforced  concrete.  The  columns  are  connected 
by  girders  and  the  space  between  the  girders  is  filled  in  with 
tile  and  joists.  When  reinforced  concrete  girders  are  used  be- 
tween the  columns,  a  slab  of  concrete  of  sufficient  width  and 
thickness  to  take  the  compression  must  be  constructed. 

Fig.  109  shows  a  section  of  a  tile  and  joist  floor.  The  terra 
cotta  tile  is  always  12  inches  in  width  and  from  4  inches  to  15 
inches  in  depth.  The  tile  is  simply  a  filler  between  the  joists 
and  is  so  much  dead  weight  to  be  carried  by  the  joists.  The 
joists  are  usually  4  inches  in  width  and  are  designed  as  T-beams ; 
the  slab  is  usually  2  to  3  inches  in  thickness.  The  reinforcing 
steel  in  the  beam  consists  of  one  bar  of  sufficient  area  for  the 
tensile  stress.  The  slab  should  be  reinforced  with  ^-inch  bars, 
24  inches  center  to  center  each  way. 

Spandrel  Beams.  In  Figs.  110  and  111  are  shown  two 
types  of  spandrel  beams.  In  each  case  the  head  of  the  window 
was  set  up  against  or  near  the  floor  slab  so  that  the  maximum 
amount  of  light  could  be  secured.  In  Fig.  110  the  spandrel  beam 
and  the  brickwork  above  are  covered  with  terra  cotta.  In  Fig. 
Ill  the  concrete  surface  is  finished  and  left  exposed,  which  is 
often  done  in  factory  buildings. 

TYPICAL  EXAMPLES  OF  REINFORCED  CONCRETE 
CONSTRUCTION  WORK 

Allman  Building,  Philadelphia.  The  seven-story  office 
building,  24  feet  9^  inches  by  122  feet  2|  inches,  was  built  for 
Herbert  D.  Allman,  at  Seventeenth  and  Walnut  Streets,  Phila- 
delphia. Baker  and  Dallett  were  the  architects.  The  building  is 
constructed  of  reinforced  concrete,  except  that  steel-core  columns 
are  carried  up  to  the  sixth  floor.  Fig.  112  shows  the  plans  of 
two  bays  of  a  floor,  the  bay  windows  occurring  in  alternate  bays: 
The  floors  are  designed  for  120  pounds  per  square  foot,  live  load. 
The  sizes  of  the  different  members  are  given  on  the  plan.  Ten- 
sile stress  in  the  reinforcing  steel  is  16,000  pounds  per  square 
inch,  direct  compression  in  the  concrete  is  500  pounds  per  square 


REINFORCED  CONCRETE 


211 


L__ 

—I        ox/*                 ^--4.  <f>            i— 
G*x/o"             4-i"t 

<j 

i 

5/ab 
J°            III     1 

Q 

e-M 

c/o. 

~^Wk 

^J?/-    Panel  <             •     1  i  p 

\           1            'O 
j  II 
MM    ^ 

r~ 

-i         8"x  ID"        4-J.  4                 r— 

|l'l| 

Slre-e?  Line 


In  Top  of  Slab 


Fig.  112.    Plan  of  Two  Bays  of  a  Floor  in  Allman  Building, 
Philadelphia,  Pennsylvania 


Line- — *j 
Fig.  113.   Footing  of  Allman  Building 


212 


REINFORCED  CONCRETE 


inch,  and  the  trans- 
verse stress  in  com- 
pression 600  pounds 
per  square  inch,  while 
the  shearing  stress  is 
75  pounds  per  square 
inch.  In  designing  the 
columns  ^in  which  the 
steel  cores  occur,  the 
radius  of  gyration  was 
taken  for  the  whole 
column ;  this  reduced 
the  working  load  to 
14,000  pounds  per 
square  inch  for  the 
steel,  nothing  being  al- 
lowed for  the  concrete 
except  the  increased 
radius  of  gyration.  The 
concrete  was  a  1:2:4 
mixture.  The  footings 
used  for  this  building 
are  shown  in  Fig.  113, 
and  the  details  of  the 
girders  in  Fig.  1J4. 
Girder  Bridge,  Allen- 


I3    town,     Pennsylvania. 


This  type  of  reinforced 
concrete  bridge,  Fig. 
115,  is  one  that  has 
been  found  to  be  eco- 
n  o  m  i  c  a  1  for  short 
spans.  Worn-out  wood 
and  steel  highway 
bridges  are  in  general 
being  replaced  with 
reinforced  concrete 


REINFORCED  CONCRETE 


213 


214  REINFORCED  CONCRETE 

bridges,  usually  at  a  cost  less  than  that  of  a  steel  bridge 
of  the  same  strength.  Steel  bridges  need  to  be  painted  every 
year;  and  plank  floors,  commonly  used  in  highway  bridges, 
require  almost  constant  attention  and  must  be  entirely  renewed 
several  times  during  the  life  of  a  bridge.  A  reinforced  concrete 
bridge,  however,  is  entirely  free  of  these  expenses,  and  its  life 
should  be  at  least  equal  to  that  of  a  stone  arch,  with  which, 
architecturally,  it  compares  very  favorably. 

The  bridge  shown  in  Fig.  115  is  16  feet  wide,  and  has  a  clear 
span  of  30  feet.  It  is  designed  to  carry  a  uniformly  distributed 
load  of  150  pounds  per  square  foot,  or  a  steel  road  roller  weigh- 
ing 15  tons  and  having  the  following  dimensions :  width  of  the 
front  roller,  4  feet,  and  of  each  rear  roller,  20  inches;  distance 
between  the  two  rear  rollers,  5  feet,  center  to  center;  distance 
between  front  and  rear  rollers,  11  feet,  center  to  center;  weight 
on  front  roller,  6  tons;  weight  on  each  rear  roller,  4.5  tons. 

In  designing  this  bridge,  the  slab  was  planned  to  carry  a  live 
load  of  4.5  tons  on  a  width  of  20  inches,  when  placed  at  the 
middle  of  the  span,  together  with  the  dead  load  consisting  of 
the  weight  of  the  macadam  and  the  slab.  The  load  considered 
in  designing  the  crossbeams  consisted  of  the  dead  load— weight 
of  the  macadam,  slab,  and  beam— and  a  live  load  of  6  tons  placed 
at  the  center  of  the  span  of  the  beam,  which  was  designed  as  a 
T-beam.  In  designing  each  of  the  longitudinal  girders,  the  live 
load  was  taken  as  a  uniformly  distributed  load  of  150  pounds 
per  square  foot  over  one-half  of  the  floor  area  of  the  bridge. 
The  live  load  was  increased  20  per  cent  over  the  live  load  given 
above,  to  allow  for  impact.  The  concrete  for  the  work  was 
composed  of  1  part  Portland  cement,  2  parts  sand,  and  4  parts 
1-inch  stone.  Corrugated  reinforcing  bars  were  used. 

In  a  bridge  of  this  type,  longitudinal  girders  act  as  a  parapet 
as  well  as  main  members  of  the  bridge.  When  there  is  suffi- 
cient headroom,  all  the  beams  can  be  constructed  in  the  longi- 
tudinal direction  of  the  bridge,  and  are  under  the  slab.  The 
parapet  may  be  constructed  of  concrete;  a  cheaper  method  is 
to  construct  a  handrailing  with  IJ-inch  or  2-inch  pipe. 

Circular  Tanks.     In  Fig.  116  is  shown  the  section  of  the 


REINFORCED  CONCRETE 


215 


< 
*! 

&- 

<r 

\ 
\ 

V 

5s- 


wall  of  four  circular  tanks,  each  of  which  is  50  feet  in  diameter. 
The  concrete  was  a  1:3:5  mix,  the  materials  being  carefully 
graded.  The  tension  in  the  steel  is  12,000  pounds  per  square 
inch.  Square  deformed  bars  were  used.  The  tanks  were  made 
water-tight  by  the  Sylvester  process. 

Main  Intercepting  Sewer,  Waterbury,  Connecticut.  In 
the  development  of  sewage  purification  work  at  Waterbury, 
Connecticut,  the  construction  of  a  main 
intercepting  sewer  was  a  necessity.  This 
sewer  is  3  miles  long.  It  is  of  horseshoe 
shape,  4  feet  6  inches  by  4  feet  5  inches, 
and  is  constructed  of  reinforced  concrete. 
The  details  are  illustrated  in  Fig.  117. 

The  trench  excavations  were  prin- 
cipally through  water-bearing  gravel, 
the  gravel  ranging  from  coarse  to  fine. 
Some  rock  was  encountered  in  the  trench 
excavations;  it  was  a  granite  gneiss  of 
irregular  fracture,  and  cost,  with  labor 
at  17|  cents  per  hour,  about  $2.00  per 
cubic  yard  to  remove  it.  Much  of  the 
trench  work  varied  in  depth  from  20 
to  26  feet.  To  suit  different  conditions, 
it  was  necessary  to  vary  the  sewer  sec- 
tion somewhat;  frequently,  the  footing 
course  was  extended.  However,  the  sec- 
tion "shown  is  the  normal  one. 
wet  concrete  was  poured  into  practically 
water-tight  forms.  The  proportions  used  were  1  part  Atlas 
Portland  cement  to  7.5  parts  of  aggregate,  graded  to  secure  a 
dense  concrete.  Care  was  used  in  placing  the  concrete,  and 
very  smooth  surfaces  were  secured.  Plastering  of  the  surfaces 
was  avoided.  Any  voids  were  grouted  or  pointed,  and  smoothed 
with  a  wooden  float.  Expanded  metal  and  square-twisted  bars 
were  used  in  different  parts  of  the  work.  'Fig.  117  shows  the 
size  and  spacing  of  the  bars,  which  were  bent  to  their  required 
shape  before  they  were  lowered  into  the  excavation. 


yerv   Fig.  116.  Typical  Sec- 
17  tion  of  Tank 


216 


REINFORCED  CONCRETE 


The  forms  in  general  were  constructed  as  shown  in  the  figure. 
The  inverted  section  was  built  as  the  first  operation  and,  after 
the  surface  was  thoroughly  troweled,  the  section  was  allowed 
to  set  36  to  48  hours  before  the  concreting  of  the  arch  section 
was  begun.  The  lagging  was  f  inch  thick,  with  tongue-and- 
groove  radial  joints,  and  toenailed  to  the  2-inch  plank  ribs. 
The  exterior  curve  was  planed  and  scraped  to  a  true  surface. 
The  vertical  sides  of  the  inner  form  are  readily  immovable,  and 


60 


-Strap  Iron 


Fig.  117.   Section  of  Intercepting  Sewer  at  Waterbury,  Connecticut 

the  semicircular  arch  above  is  hinged  at  the  soffit  and  is  col- 
lapsible. The  first  cost  of  these  forms  averaged  $18.00  for  10 
feet  of  length,  and  the  cost  per  foot  of  sewer  built,  both  first 
cost  and  maintenance,  averaged  10  cents.  Petrolene,  a  crude 
petroleum,  prevented  the  concrete  from  adhering  to  the  forms. 
Cost  records  kept  under  the  several  contracts  and  assembled 
into  a  composite  form,  show  what  is  considered  to  be  the  normal 
cost  of  this  section,  under  the  local  conditions.  Common  labor 
averaged  17£  cents,  sub-foremen  30  cents,  and  general  foremen 
50  cents  per  hour. 


REINFORCED  CONCRETE 


217 


Normal  Cost  per  Lineal  Foot  of  53=  by  54-inch  Rienforced 
Concrete   Sewer 

Steel  reinforcement,  17|  Ib $  .43 

Making  and  placing  reinforcement  cages 14 

Wood  interior  forms,  cost,  maintenance,  and  depreciation 12 

Wood  exterior  forms,  cost,  maintenance,  and  depreciation 05 

Operation  of  forms 16 

Coating  oil . 01 

Mixing  concrete 30 

Placing    concrete t 27 

Screeding  and  finishing  invert 08 

Storage,  handling,  and  cartage  of  cement 08 

0.482  bbl.  cement  at  $1.53 74 

0.17  cu.  yd.  sand  at  $0.50 09 

0.435  cu.  yd.  broken  stone  at  $1.10 : 47 

Finishing  interior  surface 01 

Sprinkling  and  wetting  completed  work 02 

Total  cost  per  lineal  foot $2.97 

This  is  equivalent  to  a  cost  of  $9.02  per  cubic  yard. 

Bronx  Sewer,  New  York  City.    Fig.  118  shows  a  section 
of  one  of  the  branch  sewers  constructed  in  the  Borough  of  the 


Fig.  118.    Section  of  Bronx  Sewer, 
New  York  City 

Bronx,  New  York  City.  A  large  part  of  this  sewer  is  located 
in  a  salt  marsh  where  water  and  unstable  soil  made  construction 
work  very  difficult.  The  general  elevation  of  the  marsh  is  1.5 
feet  above  mean  high  water.  In  constructing  this  sewer  in  the 


218  REINFORCED  CONCRETE 

marsh,  it  was  necessary  to  build  a  pile  foundation  to  support  the 
sewer.  The  foundation  was  capped  with  reinforced  concrete, 
and  then  the  sewer,  as  shown  in  the  section,  was  constructed  on 
the  pile  foundation.  The  concrete  for  this  work  was  composed 
of  1  part  Portland  cement,  2.5  parts  sand,  and  5  parts  trap 
rock.  The  rock  was  crushed  to  pass  a  f-inch  screen.  Twisted 
bars  were  used  for  the  reinforcement  in  the  work. 


APPENDIX 

FLAT=SLAB  CONSTRUCTION 

Outline  of  Method.  The  so-called  "flat-slab  method"  has 
the  advantages  that  (a)  there  is  a  very  considerable  saving  in  the 
required  height  (and  cost)  of  the  building  on  the  basis  of  a  given 
net  clear  height  between  floors;  (b)  the  architectural  appearance 
is  improved  by  having  a  flat  ceiling  surface  rather  than  visible 
beams  and  girders ;  (c)  there  is  a  saving  in  the  cost  of  forms,  not 
only  in  surface  area  and  amount  of  lumber  required  but  also 
in  simplicity  of  construction,  although  this  saving  is  offset  by 
an  increase  in  total  volume  of  concrete  used;  (d)  there  are  no 
deep  ceiling  beams  to  cast  shadows  and  it  is  possible  to  extend 
the  windows  up  to  the  ceiling,  which  are  important  items  in  the 
lighting  of  a  factory  building.  Almost  the  only  disadvantage  is 
the  difficulty  in  making  perfectly  definite  and  exact  computa- 
tions of  the  stresses,  as  may  be  done  for  simple  beams  and  slabs. 
But  methods  of  computation  have  been  devised  which,  although 
admittedly  approximate,  will  produce  designs  for  economical 
construction,  and  structures  so  designed  have  endured,  without 
distress,  test  loads  considerably  greater  than  the  designed  work- 
ing loads. 

Consider,  first,  a  simple  beam,  as  in  Fig.  119-a,  the  beam  being 
continuous  over  the  supports  and  uniformly  loaded  for  the  dis- 
tance I  between  the  supports  with  a  load  amounting  to  W.  Then 
the  maximum  moment  is  located  just  over  the  supports  and 
equals  Wl  -^  12.  Another  local  maximum,  equal  to  Wl  -*-  24,  is 
found  at  the  center.  Points  of  inflection  are  at  .211Z  from  each 
column. 

Assume  that  a  uniformly  loaded  plate  of  indefinite  extent  is 
supported  on  four  columns,  A,  B,  C,  and  D,  Fig.  119-b,  the 
extensions  beyond  the  columns  being  such  that  planes  tangent 
to  the  plate  just  over  the  columns  will  be  horizontal.  Then 

219 


220 


REINFORCED  CONCRETE 


Wl 
~72 


Wl 
7z 


TTT 

.        ^    .£//.    „. 
COLUMN     (p)  COLUMN. 


\ 


Fig.  110.    Flat-Slab  Construction 


the  following  conditions  may 
be  observed : 

(1)  The  plate  will  be  con- 
vex   upward    over    the    col- 
umns; 

(2)  The  plate  will  be  con- 
cave upward  at  the  point  0 
in  the  center; 

(3)  There  will  be  curves 
of  inflection,  approximately 
as  shown  by  the  dotted  curves 
sketched  in  around  the  col- 
umns; from  the  analogy  of 
the  simple  beam,  given  above, 
wa    may    assume    that    the 
curves  of  inflection  are  ap- 
proximately at  21  per  cent  of 
the  span  in  every  direction 
from  the  columns. 

The  columns  at  the  top  are 
made  with  enlarged  sections 
so  as  to  form  a  "column 
head"— which  is  generally  in 
the  form  of  a  frustum  of  an 
inverted  pyramid  or  cone, 
the  base  being  a  circle,  a 
square,  or  a  regular  polygon. 

This  device  shortens  the 
clear  span  and  decreases  the 
moment.  It  also  increases 
the  size  of  the  hole  which  the 
column  tends  to  punch 
through  the  plate  and  hence 
increases  the  surface  area 
which  resists  this  punching 
shear,  and  thus  decreases 
the  unit  shear.  The  diam- 


REINFORCED  CONCRETE  221 

eter  of  the  column  head  should  be  about  25  per  cent  of  the 
span  between  column  centers. 

Placing  Reinforcing  Bars.  Various  systems  of  placing  the 
reinforcing-  bars  have  been  devised,  and  some  of  them  patented. 
The  methods  may  be  classified  as  follows:  (1)  "Four-way" 
method,  in  which  the  bars  run  not  only  in  lines  parallel  to  the 
sides  of  the  rectangles  joining  the  column  heads,  but  also  par- 
allel to  the  diagonals,;  (2)  "two-way"  method,  in  which  there 
are  no  diagonal  bars;  and  (3)  designs  which  have,  in  addition 
to  the  bands  of  straight  bars  from  column  to  column,  spirals 
or  a  series  of  rings  around  the  column  heads  for  the  specific 
purpose  of  providing  for  the  "circumferential  tension,  or  mo- 
ment." This  circumferential  tension  unquestionably  exists,  but 
those  who  use  the  first  two  methods  claim  that  the  gridiron  of 
bars  formed  over  the  column  by  the  two-way  method,  and  still 
more  so  by  the  four-way  method,  develops  plate  action,  and  that 
the  circumferential  stress  is  amply  provided  for. 

It  is  a  simple  matter  of  geometry  to  prove  that  .if  bands  of 
bars  of  width  I),  Fig.  119-b,  are  placed  across  columns  which 
form  square  panels  with  span  /,,  the  width  b  must  equal  .414Z,  if 
the  bands  exactly  cover  the  space  without  leaving  either  gaps 
or  overlaps  at  m,  n,  o,  and  p.  The  bands  may  be  a  little  nar- 
rower than  this,  say  b  equals  Al,  provided  the  gaps  are  not 
much,  if  any,  greater  than  the  spacing  of  the  bars.  On  the  other 
hand,  the  bands  should  not  be  wider  than  twice  the  diameter  of 
the  column  head.  Fig.  119-c  shows  that,  using  the  four-way 
system  and  with  b  equal  to  .4147,  every  part  of  the  slab  has  at 
least  one  layer  of  bars,  some  parts  have  two,  some  three,  and  that 
there  are  four  layers  of  bars  over  each  column.  This  is  where 
the  moment  is  maximum. 

Method  of  Calculation.  One  of  the  simplest  methods  of 
calculation,  which  probably  gives  a  considerable  but  indeter- 
minate excess  of  strength,  is  to  consider  the  bands  as  so  many 
simple  continuous  beams,  which  are  wide  but  shallow.  Consider 
a  direct  band  of  width  b,  equal  to  Al,  the  word  direct  being  used 
in  contradistinction  to  diagonal.  If  w  is  the  unit  dead  and  live 
load  per  square  foot,  and  s  the  net  span  between  column  heads, 


222  REINFORCED  CONCRETE 

then  the  total  load  on  the  band  is  Aids.  Computed  as  a  simple 
continuous  beam,  the  moment  in  the  center  would  be  (Awls) 
s  -*-  24,  and  that  over  the  columns  would  be  (Awls)  s  -+- 12.  By 
prolonging  the  steel  bars  of  adjoining  bands  sufficiently  over  a 
column  head  so  that  the  bond  adhesion  is  sufficient  to  develop  the 
full  tension  over  the  column  head,  the  total  effective  area  of  steel 
in  that  band  over  the  column  head  is  double  what  it  is  in  the 
center.  Practically,  this  means  that  the  steel  should  extend  to 
the  point  of  inflection  beyond  the  column  head  or  that  its  length 
should  be  42  per  cent  longer  than  the  distance  between  column 
centers.  Then,  on  the  principle  of  T-beam  flanges,  it  is  assumed 
that  the  concrete  above  the  neutral  axis  for  a  width  of  (b  +  5t) 
may  be  computed  as  taking  the  compression.  For  the  diagonal 
bands,  the  load  is  w  X  Al  X  1.414s  =  .565wls,  and  then,  consid- 
ering that  a  considerable  part  of  the  area  of  the  diagonal  bands 
includes  that  already  covered  by  the  direct  bands,  and  also  that 
the  diagonal  bands  both  support  a  square  in  the  center  which  is 
one-half  of  the  area  lying  inside  of  the  direct  bands,  the  moment 
for  the  central  area  is  divided  between  the  two  diagonal  bands 
and  that  for  each  is  considered  to  be  (.5G5wls  X  1.414s)  -*- 48 
=  .016GwZs2.  As  before,  the  moment  over  the  columns  for  these 
bands  is  twice  as  much,  but  the  steel  for  the  double  moment  may 
be  obtained,  as  before,  by  lapping  the  bars  of  adjoining  diagonal 
bauds  over  the  columns.  The  area  of  a  panel,  outside  of  the 
column  heads,  which  are  here  assumed  to  be  square,  is 
l~ — (I  —  s)2.  When  the  column  head  is  25  per  cent  of  I, 
then  (I  —  s)=iZ  and  the  area  of  the  panel  is  il/2,  or  .9375Z2; 
and  the  total  effective  load  causing  moment  on  a  panel  is 
W  =  .9375-M/Z2.  If  we  eliminate  s  and  w  from  the  above  moment 
equations,  we  have 

Moment  at  center,  direct  band 

_  (Awls)s  __  Awl3  i9e  _  3.6      a_  Wl 
~24~       ~~24~  =384W'     =  lOO" 

Moment  over  cap,  direct  band  =  (double  the  above)  =  Wl  -*-  50 
Moment  at  center,  diagonal  band  =  .OlGGw/s2  =  Wl  -*- 100 
Moment  over  cap,  diagonal  band  =  (double  the  above)  =  Wl  •*•  50 


REINFORCED  CONCRETE  223 

Illustrative  Example.  Assume  a  live  load  of  200  pounds 
per  square  foot  on  a  square  panel  22  feet  between  column  cen- 
ters. A  working  rule  is  that  the  thickness  of  the  slab  should 
be  at  least  -fa  of  the  span;  ^.  of  22  feet,  or  264  inches,  is  8.8 
inches.  We  will  therefore  assume  the  slab  thickness  as  10 
inches,  which  will  weigh  120  pounds  per  square  foot.  Therefore, 
w  =  320  and  W  =  Hwl2  =  iS  X  320  X  222  =  145,200.  Then  the 
moment  at  the  center  of  a  direct  band  equals  Wl  -*- 100  — 
(145,200  X  264) -s-  100  =  383,328  inch-pounds,  and  the  moment 
for  that  band  over  the  column  is  766,656  inch-pounds.  The 
width  of  each  band  b  is  Al  =  .4  X  264  =  105.6  inches.  Assume 
that  the  steel  for  one  of  the  bands  is  placed  at  8.5  inches  from 
the  compression  face,  or  that  d  =  8.5 ;  if  we  estimate  j  =  .91  j 
then 

M  =  383,328 
=  pbdsjd 

=  pX  105.6  X  8.5  X  16,000  X  .91  X  8.5 
from  which 

p  =  .00345 

From  Table  XII,  we  may  note  that  for  n  =  15  and  p  =  .00345, 
,;*  would  be  about  .91.  This  checks  the  assumed  value.  Then 

A  =  pbd  =  .00345  X  105.6  X  8.5  =  3.10  sq.  in. 

This  may  be  amply  provided  by  13  bars  i  inch  square.  105.6 
-*- 12,  or  about  9  inches,  gives  the  spacing  of  the  bars.  Al- 
though doubling  p  changes  the  value  of  j  and  will  not  exactly 
double  the  moment,  yet  it  will  be  sufficiently  exact  to  say  that 
double  the  moment  will  be  obtained  over  the  cap  by  prolonging 
the  13  bars  of  each  of  the  two  direct  bands  in  the  same  line  over 
the  columns  as  far  as  the  circle  of  inflection,  thus  doubling  the 
area  of  the  steel.  (The  student  should  work  this  out  as  an 
exercise.)  Double  p  and  find  the  corresponding  value  of  j  from 
Table  XII ;  use  the  actual  area  of  the  26  bars  for  the  value  of 
A,  and  compute  M  from  Asjd.  On  account  of  the  slight  excess 
in  the  area  of  the  26  bars  here  used,  the  moment  is  a  little 
more  than  necessary. 


224  '  REINFORCED  CONCRETE 

Location  of  Bars.  There  are  four  layers  of  bars  over  the 
column  head  and  it  is  evident  that  they,  cannot  all  lie  in  the 
same  plane  or  be  at  the  same  distance  from  the  compression 
face.  For  the  layer  of  bars  considered  above,  d  was  assumed 
at  8.5,  the  maximum  permissible  with  a  10-inch  slab.  For  the 
next  row  deduct  £  inch,  the  thickness  of  the  bars,  and  let  d  equal 
8.0.  Since  the  moment  is  the  same,  and  d  is  reduced,  then  p 
must  be  increased  and  j  will  be  less.  Assume  j  =  .90 ;  then 

M  =  383,328 
—  pbdsjd 

=  p  X  105.6  X  8  X  16,000  X  .9  X  8 
from  which 

p  =  .00394 

This  is  a  little  more  than  for  the  other  band,  as  was  expected. 
Then  A  =  pbd  =  3.33  square  inches,  provided  by  14  bars  £  inch 
square.  Similarly,  it  may  be  shown  that  reducing  d  another 
half -inch  for  the  next  layer  will  add  another  bar,  making  15 
bars  for  the  third  layer  and  16  bars  for  the  fourth  layer.  Since 
the  computed  moments  for  the  direct  and  diagonal  bands  is  the 
same  for  the  center  of  the  band,  and  since  the  diagonal  bands 
are  the  longer,  there  will  be  some  economy  in  giving  them  the 
advantageous  position  in  the  slab  (larger  values  of  d)  and  using 
13  and  14  bars  for  the  diagonal  bands  and  15  and  16  bars  for 
the  direct  bands.  The  above  variation  in  the  number  of  bars 
with  the  change  in  d  indicates  the  importance  of  placing  the 
steel  exactly  as  called  for  by  the  plans.  The  design  might  be 
made  a  little  more  symmetrical,  and  more  foolproof  during 
construction  by  using. 14  bars  in  each  of  the  diagonal  bands  and 
16  bars  in  each  of  the  direct  bands,  and  then  being  sure  that 
the  direct  bands  are  under  the  diagonal  bands  where  they  pass 
over  the  column  heads. 

Unit  Compression.  The  unit  compression  may  be  computed 
from  the  equation 

M  =  i  cb'kdjd 

For  the  concrete  compression,  we  may  call  b'  =  105.6  +  5t  = 


REINFORCED  CONCRETE  225 

105.6  H-  50  =  155.6.  The  critical  place  is  over  the  column. 
Here,  where  the  moment  is  double, 

p  =  A-*~  I'd  =  6.5  -*-  (155.6  X  8.5)  -  .00724 
Then  M  =  766,656 ;  k  —  .369 ;  and  j  =  -88. 
Substituting  these  values,  we  find  that 

c  =  420  Ib.  per  sq.  in. 

But  this  is  a  more  favorable  ease  than  the  compression  com- 
puted for  the  band  whose  d  is  only  7  inches.  In  this  case, 
p  =  A  +  bd  =  8+  (155.6  X  7)  =  .00734,  which  makes  k  =  .371 

and  j  =  .88. 

Substituting  these  values,  we  find  that 

c  =  616  Ib.  per  sq.  in. 

This  is  amply  safe,  especially  in  view  of  the  fact  that  a  cube 
subjected  to  compression  on  all  six  faces,  as  it  is  in  this  case, 
can  stand  a  far  higher  unit  compression  than  it  can  when  the 
compression  is  only  on  two  faces. 

Shear.  The  cap  is  a  square  66  inches  on  a  side  and  its  perim- 
eter is  264  inches.  V  in  this  case  equals  W  and  is  145,200 
pounds.  For  this  calculation  let  j  equal  .88  and  d  equal  8.5; 
then 

V  145,200 

*  =  bjd  =  264  X  .88  X  8.5  =  73'5  lb'  per  Sq'  in* 

Since  this  is  a  punching  shear  rather  than  diagonal  tension,  this 
Working  value  is  allowable.  The  usual  allowed  unit  value  is  80. 
At  any  section  farther  away  from  the  column  head,  the  total 
shear  is  less,  and  the  perimeter,  and  hence  the  shearing  area, 
is  greater,  and  therefore  the  unit  shear  becomes  less  and  less. 
The  zone  around  the  column  head  is  the  critical  section  and, 
since  it  is  where  the  moment  is  also  maximum,  no  main  reinforc- 
ing bars  can  be  spared  to  resist  this  shear,  as  is  done  at  the  ends 
of  simple  beams.  A  ring  of  stirrups  around  each  column  head 


226  REINFORCED  CONCRETE 

is  the  only  practicable  method  of  resisting  such  shear,  if  it  is 
excessive. 

Wall  Panels.  The  above  calculations  are  virtually  for  in- 
terior panels,  or  for  those  where  the  loads  are  balanced  over  the 
columns.  When  panels  are  next  to  a  wall,  the  bands  perpendic- 
ular to  the  wall,  and  even  the  diagonal  bands,  must  be  anchored 
by  bending  them  down  into  the  columns.  The  extra  steel  is  just 
as  necessary,  in  order  to  develop  the  moment  at  the  column 
head,  as  if  the  bands  were  extended  into  an  adjoining  panel. 
The  band  along  the  wall  between  the  wall  columns  may  have 
part  of  the  usual  width  cut  off.  In  addition  to  the  floor  load, 
the  weight  of  the  wall  makes  an  additional  load.  This  may  be 
most  efficiently  supported  by  a  "spandrel  beam",  which  is  a 
narrow  but  deep  beam  extending  up  from  the  floor  to  the 
window  sill,  and  which  virtually  forms  that  part  of  the  wall, 
although  there  may  be  an  outside  facing.  Sometimes  the  exte- 
rior columns  are  set  in  from  the  building  line  so  as  to  balance 
partially,  if  not  entirely,  the  load  on  the  other  side  of  the 
columns. 

General  Constructive  Details.  The  column  head  should  have 
a  considerable  thickness  at  its  edge,  immediately  under  the  slab, 
to  enable  it  to  withstand  shear,  as  shown  in  Fig.  119-d.  If,  as 
is  sometimes  done,  the  sloping  sides  of  the  head  are  continued 
to  the  slab  surface,  a  considerable  deduction  should  be  made 
in  estimating  the  effective  diameter  of  the  head,  which  means  an 
increase  in  the  net  span  between  columns.  The  four  points 
marked  i,  Fig.  119-d,  are  at  about  20  per  cent  of  the  net  span 
between  column  heads  and  are  the  computed  points  of  inflection 
where  there  is  no  moment.  The  bars  should  be  in  about  the 
middle  of  the  slab  at  these  points.  They  should  be  at  the 
minimum  permissible  distance  above  the  bottom  of  the  slab  at 
0  and  similarly  near  the  top  of  the  slab  at  the  edges  and  across 
the  column  heads.  There  should  not  be  abrupt  bends  at  these 
points,  but  the  bars  should  have  easy  curves  through  the  re- 
quired positions  at  0  and  the  points  of  inflection  and  then, 
reversing  curvature  so  that  it  will  be  concave  downward,  should 
again  reach  a  horizontal  direction  just  over  the  edge  of  the 


REINFORCED  CONCRETE  227 

column  head.  While  no  great  precision  is  essential  in  locating 
the  bars  between  these  specified  places,  care  must  be  taken  to 
fasten  the  bars  in  exact  position  at  the  critical  points  so  that 
they  cannot  be  disturbed.  There  should  always  be  at  least  one 
inch  of  concrete  below  the  bars  in  the  center  of  the  slab. 

Rectangular  Panels.  The  flat-slab  method  of  construction 
is  most  economically  used  when  the  panels  are  nearly,  if  not 
quite,  square,  and  also  when  the  column  spacing  can  be  made 
about  23  feet.  The  ratio  of  length  to  breadth  for  rectangular 
panels  should  not  exceed  4 : 3.  The  two  pairs  of  direct  bands 
must  then  be  computed  independently  and  separately.  The 
diagonal  bands  must  be  computed  according  to  their  actual 
dimensions,  which  means  that  the  moment  equations  given  above 
will  not  apply,  and  other  equations,  computed  in  the  same 
general  manner,  must  be  derived.  The  quantity  b  may  be 
considered  as  0.4  of  the  mean  of  the  two  column  spans.  The 
economy  of  the  flat-slab  method  is  chiefly  applicable  to  heavy 
floor  loadings,  such  as  are  required  for  factories,  warehouses, 
etc. 


INDEX 


INDEX 

A 

PAGO 

Acid  treatment  of  concrete 197 

Advantages  of  flat  slab  construction 233 

Alum  and  soap 37 

Allman   Building 210 

American  Society  on  testing  materials,  report  of 3 

Asphalt    38 

B 

Beam  design,  reinforced   concrete 50 

calculation,    practical 67 

flexure    * 50 

T-beam  construction 86 

Beams  and  slabs,  practical  calculation  and  design  of...  67 

bonding  steel  and  concrete 74 

bond  required  in  bars,  computation  of 77 

deformed  bars,  virtue  of 75 

resistance  to  slipping  of  steel. 74 

failure  by  shear  or  by  diagonal  tension 79 

I-beams,  slabs  on 83 

related  factors,  calculations  by  diagrams  of 80 

simple  beam  computation,  table  for 72 

slab  computations,  tables  for 67 

slabs  reinforced  in  both  directions 84 

temperature  cracks,  reinforcement  against 85 

vertical  shear  and  diagonal  tension 78 

Bending  or  trussing  bars 201 

bars,  slab 203 

column  bands v , 204 

229 


230  REINFORCED  CONCRETE 

Bending  or  trussing  bars  (Continued)  PAGB 

details 201 

hooked  ends,  bars  with 203 

spacers '204 

stirrups 204 

tables 202 

unit  frames . : 206 

Bonding  old  and  new  concrete. 33,  206 

Broken  stone 10 

classification    10 

sizes 10 

( 

C 

Canal  Dover,  Ohio,  bridge  at 190 

Cement 1 

classification 2 

natural 2 

Portland  2 

standard  specifications 3 

Cement  brick „ 158 

Cement  lime  mortar 13 

Cement-brick  machines 178 

Cinder  concrete 19 

Cinders 12 

Column  bands 204 

Common  lime  mortar 12 

Composition  of  concrete  and  reinforced  concrete 1 

broken  stone 10 

cement « . 1 

concrete  mixtures,  characteristics  and  properties  of  14 

fire  •protective  qualities 43 

mixing  and  laying. . .  •. 21 

mortars * .  * 12 

preservation  of  steel  in  concrete 41 


REINFORCED  CONCRETE  231 

Composition  of  concrete  (Continued)  PAGR 

sand '6 

steel  for  reinforcing  concrete 45 

waterproofing 35 

Compound  footings Ill 

conditions  demanding •  111 

problem,  practical  treatment  of 112 

Concrete  and  reinforced  concrete ,1 

beam  design f 50 

composition  and  treatment 1 

construction   work 170 

miscellaneous  designs 104 

Concrete  building  blocks .- 154 

cost    157 

curing   157 

air   157 

steam 157 

materials 156 

mixing  and  tamping 156 

sizes 155 

types  155 

Concrete  construction  work 170 

bending  or  trussing  bars 201 

bonding  old  and  new  concrete 206 

examples,  typical 210 

forms ... 180 

machinery    170 

spandrel  beams 210 

steel  cores 208 

surfaces  of  concrete,  finishing 193 

tile  of  joist  system 209 

Concrete  curb "... 166 

construction » 167 

cost    , 169 

types   ,. 167 


232  REINFORCED  CONCRETE 

PAGE 

Concrete  designs,  miscellaneous 104 

building  blocks 154 

compound  footings Ill 

culverts 145 

curbs  ; . .  166 

fence   posts 158 

girder  bridges 150 

piles H6 

retaining  walls.  .^ [ .  123 

silos , . . ." 160 

simple  footings 104 

walks    161 

Concrete  mixtures,  characteristics  and  properties  of 14 

compressive.  strength 15 

cost 18 

broken  stone  or  gravel 18 

cement    18 

forms 18 

mixing 18 

sand    18 

elasticity,  modulus  of 17 

principles  used   in  proportioning 14 

ideal  conditions 14 

practice,  conditions  in 15 

standard   proportions    15 

shearing  strength    17 

standard  aggregate,  variations  from 19 

cinder  concrete , 19 

rubble   concrete    19 

tensile   strength 17 

weight    18 

Concrete  walks 161 

base 162 

cost    : 165 

foundations,  drainage 161 


REINFORCED  CONCRETE  233 

Concrete  walks  (Continued) 


seasonng    ......................................  165 

top  surface  .....................................  163 

Concrete-block  machines  .............................  177 

Culverts   ...........................................   145 

loadings,  classification  by  ........................  145 

D 
Dry  concrete  .................................  25 

E 

Examples  of  reinforced  concrete  construction  work  .....  210 

Allentown,  Pennsylvania,  girder  bridge  at  .........  211 

Allman  Building,  Philadelphia  ...................  210 

circular  tanks  ..................................  213 

New  York  City,  Bronx  sewer  .....................  217 

Waterbury,  Connecticut,  intercepting  sewer  at  ......  215 

F 

Fence  posts  ........................................  158 

design    ..............  ...........................  158 

fastenings    .  ....................................  159 

materials  and  forms  ............................  160 

Finishing  surfaces  of  concrete  ........................  193 

acid  treatment  .........  .  .......................  197 

cast  -slab  veneer  ................................  198 

concrete  finish,  colors  for  ........................  199 

concrete  surfaces,   painting  .......................  199 

dry  mortar  finish  ...............................  198 

efflorescence   ....................................  200 

floors,  finish  for  .......  .  .  .  ........................  199 

granolithic   .............................  ........  197 

hammer  dressing  ...................  ..............  196 

imperfections    ..................................  193 

laitance  .................  ,  ......................  201 


234  REINFORCED  CONCRETE 

Finishing'  surfaces  of  concrete  (Continued)  PAGE 

masonry  facing 195 

moldings  and  ornamental  shapes 199 

mortar  facing  194 

plastering    194 

Fire  protective  qualities  of  concrete 43 

Baltimore  fire,  results  in 45 

cinder  vs.   stone   concrete 44 

high  resisting  qualities 43 

theory   44 

thickness  of  concrete  required 43 

Flat  slab  construction 219 

advantages 233 

placing  reinforcing  bars    235 

method   of  calculation 235 

location  of  bars  237 

general  constructive  details 240 

economical  span  240 

Flexure  of  beam  design • 50 

plain  homogeneous  beams,  statics  of .  .  51 

reinforced  concrete  beams,  statics  of 53 

compressive  forces,  center  of  gravity  of 56 

compressive  forces,  summation  of 55 

elasticity  in  compression   54 

neutral  axis , .  56 

ratio  of  moduli  of  elasticity,  values  of 57 

resisting  moment   61 

steel,  percentage  of 60 

theoretical  assumptions    , 54 

theory  50 

Forms 180 

building 180 

beams  and  slabs,  for 183 

columns,  for   183 

cost    184 


REINFORCED  CONCRETE  235 

Forms  (Continued)  PAGB 

centers  of  arches,  for  ...................  .........  187 

bridge  at  Canal  Dover,  Ohio  ..................  190 

classes  .....................................  188 

175th  Street  Arch,  New  York  City  .........  ....  189 

sewers  and  walls,  for  ............................  .185 

conduits  and  sewers  .........................  185 

Torresdale  filters   ____  .........  .  .............  185 

Freezing  concrete    ...............  .........  ;  .........     33 

G 
Girder  bridges    .....................  .  .........  .....  .  150 

H 
Havemeyer  bar  .....................................     48 

K 
Kahn  bar  ..............................  »  .  .  .........     48 


Machinery  for  concrete  work  ................  .  ........  170 

cement-brick  machines   ...  .......................  178 

concrete-block  machines  .........................  177 

hoisting  and  transporting  equipment  ..............  173 

concrete    ...................................  174 

electric  power  .  .  .  ..................  ........  ,  173 

lumber  and  steel   .........................  .  .  174 

mixers,  charging    .......  ....................  174 

plant  for  street  work.  .  .  .  ..........  ..........  175 

mixers  ...........  ..............................  170 

batch  ...............  ....  ...................  172 

continuous    .................................  171 

power,  sources  of  .........  /  ..................  172 

plant    ..................  .......................  .  170 

saiid-washing    ............  :  ----  *  ----  •  ...........  179 


236  REINFORCED  CONCRETE 

PAGE 

Medium  concrete 26 

Mixing  and  laying  concrete 21 

methods 27 

hand,  by  27 

machinery,  by  28 

machine  vs.  hand  29 

problems  in  laying  concrete 29 

bonding  old  and  new 33 

depositing  under  water 31 

freezing,  effects  of 33 

ramming 30 

transporting  arid  depositing  . . , 29 

proportioning 21 

lean  mixture 21 

medium  mixture 21 

ordinary  mixture  ; .  21 

rich  mixture 21 

wetness  of  concrete  25 

modern  practice  26 

Modulus  of  elasticity  ....;„ 17 

Mortars  12 

common  lime 12 

natural  cement 13 

Portland  cement 13 

N 

Natural  cement 2,  4,    13 

New  York  City,  arch  at  175th  Street 189 

P 

Piles 116 

capping  and  driving 117 

concrete  and  reinforced  concrete,  advantage 116 

cost    122 

design 118 

loading 119 


REINFORCED  CONCRETE  237 

Piles  (Continued)  PAGE 

types 119 

Raymond  concrete 120 

simplex  concrete 121 

Portland  cement  2,  5,  13,    18 

R 

Ramming  concrete  30 

Raymond  concrete  pile 120 

Reinforced  concrete  walls  132 

Resisting  moment 61 

Retaining  walls 123 

design 126 

base,  width  of 127 

coping  and  anchorages 145 

counterforts,  reinforced  concrete  walls  with. . . .  139 

face 126 

methods    126 

pressure  behind 127 

pressure  on  foundation 129 

reinforced  concrete 132 

failures 124 

fill 126 

foundations    125 

Rubble  concrete 19 

S 

Sand 6 

geological  character 7 

qualities    7 

cleanness    8 

coarseness    . . 7 

sharpness r. * . , 8 

value  6 

voids,  percentage  of 9 


238  REINFORCED  CONCRETE 

PAGE 

Sand-washing 179 

Shearing  strength 17 

Silos    ; 160 

design IGQ 

types   160 

Simple  footings 104 

column    4. 106 

continuous  beam in- 
reinforced  concrete,  effectiveness  of 104 

wall 104 

Simplex  concrete  pile  121 

Slab  bars 203 

Slag  . .  f 11 

Spacers , 204 

Spandrel  beams   210 

Steel  bars    , 46 

deformed    . , 47 

corrugated    47 

Havemeyer    48 

Kahn  48 

square  twisted 47 

plain 46 

st6el  sections 47 

Steel  cores 208 

Steel  for  reinforcing  concrete 45 

bars  used,  types  of 46 

deformed    . .  •. 47 

expanded  metal   49 

plain    46 

quality 45 

hard ,  46 

medium  '. .     45 

soft    . , 45 


REINFORCED  CONCRETE  239 

PAGE 

Steel  in  concrete,  preservation  of 41 

cinder  vs.  stone  concrete 42 

illustrations 42 

tests,  short-time  41 

Stirrups 204 

.     T 
Tables  — 

barrels  of  Portland  cement  per  cubic  yard  of  mor- 
tar     -.23,  24 

bond  adhesion  of-  plain  and  deformed  bars  per  one 

inch  of  length 76 

cement,  sand,  and  stone  in  actual  structures,  propor- 
tions of 22 

compressive  strength  of  concrete 16 

compressive  tests  of  concrete 17 

gross  load  on  rectangular  beam  one  inch  wide 73 

ingredients  in  one  cubic  yard  of  concrete. ...... .24,  25 

modulus  of  elasticity  of  some  grades  of  concrete. . .  60 

required  width  of  beam 92 

standard  sizes  of  expanded  metal 49 

tensile  test  of  concrete 29 

value  of  j  for  various  values  of  n  and  p. 58 

value  of  k  for  various  values  of  n  and  p 57 

value  of  p  for  various  values  of  (s  -*-  c)  and  n 62 

working  loads  on  floor  slabs , 68,  69,  70 

weights  and  areas  of  square  and  round  bars 50 

T-beam  construction 86 

flange,  width  of 90 

resisting  moments 87 

rib,  width  of 91 

shear  in  T-beam 96 

shearing  stresses  . 93 

slab,  beam,  and  girder  construction,  illustration  of. .  97 

Tensile  strength 17 


240  REINFORCED  CONCRETE 

PAGE 

Tile  and  joist  system 209 

Torresdale  filters,  forms  of .. 185 

Transporting  and  depositing  concrete 29 

U 

Unit  frames 206 

W 

Waterproofing , 35 

concrete  not  generally  water-tight 35 

methods  35 

alum  and  soap 37 

asphalt 33 

felt  laid  with  asphalt  or  coal  tar 39 

hydrated  lime  '37 

linseed  oil  37 

plastering 36 

Sylyester  process  38 

Wet  concrete   .     . ... 26 


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